id	sid	tid	token	lemma	pos
ejpam-2979	1	1	european	european	PROPN
ejpam-2979	1	2	journal	journal	PROPN
ejpam-2979	1	3	of	of	ADP
ejpam-2979	1	4	pure	pure	ADJ
ejpam-2979	1	5	and	and	CCONJ
ejpam-2979	1	6	applied	apply	VERB
ejpam-2979	1	7	mathematics	mathematic	NOUN
ejpam-2979	1	8	vol	vol	NOUN
ejpam-2979	1	9	.	.	PROPN
ejpam-2979	2	1	10	10	NUM
ejpam-2979	2	2	,	,	PUNCT
ejpam-2979	2	3	no	no	INTJ
ejpam-2979	2	4	.	.	NOUN
ejpam-2979	2	5	3	3	NUM
ejpam-2979	2	6	,	,	PUNCT
ejpam-2979	2	7	2017	2017	NUM
ejpam-2979	2	8	,	,	PUNCT
ejpam-2979	2	9	506	506	NUM
ejpam-2979	2	10	-	-	SYM
ejpam-2979	2	11	515	515	NUM
ejpam-2979	2	12	issn	issn	PROPN
ejpam-2979	2	13	1307	1307	NUM
ejpam-2979	2	14	-	-	SYM
ejpam-2979	2	15	5543	5543	NUM
ejpam-2979	2	16	–	–	PUNCT
ejpam-2979	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2979	2	18	published	publish	VERB
ejpam-2979	2	19	by	by	ADP
ejpam-2979	2	20	new	new	PROPN
ejpam-2979	2	21	york	york	PROPN
ejpam-2979	2	22	business	business	PROPN
ejpam-2979	2	23	global	global	PROPN
ejpam-2979	2	24	on	on	ADP
ejpam-2979	2	25	identities	identity	NOUN
ejpam-2979	2	26	for	for	ADP
ejpam-2979	2	27	sequences	sequence	NOUN
ejpam-2979	2	28	of	of	ADP
ejpam-2979	2	29	binomial	binomial	ADJ
ejpam-2979	2	30	sums	sum	NOUN
ejpam-2979	2	31	with	with	ADP
ejpam-2979	2	32	the	the	DET
ejpam-2979	2	33	terms	term	NOUN
ejpam-2979	2	34	of	of	ADP
ejpam-2979	2	35	sequences	sequence	NOUN
ejpam-2979	2	36	{	{	PUNCT
ejpam-2979	2	37	ukn	ukn	NOUN
ejpam-2979	2	38	}	}	PUNCT
ejpam-2979	2	39	and	and	CCONJ
ejpam-2979	2	40	{	{	PUNCT
ejpam-2979	2	41	vkn	vkn	NOUN
ejpam-2979	2	42	}	}	PUNCT
ejpam-2979	2	43	neşe	neşe	ADJ
ejpam-2979	2	44	ömür1,∗	ömür1,∗	NOUN
ejpam-2979	2	45	,	,	PUNCT
ejpam-2979	2	46	cemile	cemile	ADJ
ejpam-2979	2	47	duygu	duygu	NOUN
ejpam-2979	2	48	şener1	şener1	PUNCT
ejpam-2979	2	49	1	1	NUM
ejpam-2979	2	50	mathematics	mathematics	NOUN
ejpam-2979	2	51	department	department	NOUN
ejpam-2979	2	52	,	,	PUNCT
ejpam-2979	2	53	science	science	NOUN
ejpam-2979	2	54	and	and	CCONJ
ejpam-2979	2	55	art	art	NOUN
ejpam-2979	2	56	faculty	faculty	NOUN
ejpam-2979	2	57	,	,	PUNCT
ejpam-2979	2	58	kocaeli	kocaeli	PROPN
ejpam-2979	2	59	university	university	PROPN
ejpam-2979	2	60	,	,	PUNCT
ejpam-2979	2	61	turkey	turkey	PROPN
ejpam-2979	2	62	abstract	abstract	NOUN
ejpam-2979	2	63	.	.	PUNCT
ejpam-2979	3	1	in	in	ADP
ejpam-2979	3	2	this	this	DET
ejpam-2979	3	3	paper	paper	NOUN
ejpam-2979	3	4	,	,	PUNCT
ejpam-2979	3	5	considering	consider	VERB
ejpam-2979	3	6	technique	technique	NOUN
ejpam-2979	3	7	used	use	VERB
ejpam-2979	3	8	in	in	ADP
ejpam-2979	3	9	[	[	X
ejpam-2979	3	10	4	4	NUM
ejpam-2979	3	11	]	]	PUNCT
ejpam-2979	3	12	,	,	PUNCT
ejpam-2979	3	13	and	and	CCONJ
ejpam-2979	3	14	the	the	DET
ejpam-2979	3	15	sequences	sequence	NOUN
ejpam-2979	3	16	{	{	PUNCT
ejpam-2979	3	17	ukn	ukn	NOUN
ejpam-2979	3	18	}	}	PUNCT
ejpam-2979	3	19	and	and	CCONJ
ejpam-2979	3	20	{	{	PUNCT
ejpam-2979	3	21	vkn	vkn	NOUN
ejpam-2979	3	22	}	}	PUNCT
ejpam-2979	3	23	,	,	PUNCT
ejpam-2979	3	24	we	we	PRON
ejpam-2979	3	25	derive	derive	VERB
ejpam-2979	3	26	the	the	DET
ejpam-2979	3	27	sequences	sequence	NOUN
ejpam-2979	3	28	{	{	PUNCT
ejpam-2979	3	29	gkn	gkn	NOUN
ejpam-2979	3	30	}	}	PUNCT
ejpam-2979	3	31	and	and	CCONJ
ejpam-2979	3	32	{	{	PUNCT
ejpam-2979	3	33	hkn	hkn	NOUN
ejpam-2979	3	34	}	}	PUNCT
ejpam-2979	3	35	.	.	PUNCT
ejpam-2979	4	1	also	also	ADV
ejpam-2979	4	2	with	with	ADP
ejpam-2979	4	3	the	the	DET
ejpam-2979	4	4	aid	aid	NOUN
ejpam-2979	4	5	of	of	ADP
ejpam-2979	4	6	generating	generate	VERB
ejpam-2979	4	7	matrix	matrix	NOUN
ejpam-2979	4	8	for	for	ADP
ejpam-2979	4	9	the	the	DET
ejpam-2979	4	10	terms	term	NOUN
ejpam-2979	4	11	of	of	ADP
ejpam-2979	4	12	these	these	DET
ejpam-2979	4	13	sequences	sequence	NOUN
ejpam-2979	4	14	for	for	ADP
ejpam-2979	4	15	a	a	DET
ejpam-2979	4	16	positive	positive	ADJ
ejpam-2979	4	17	integer	integer	NOUN
ejpam-2979	4	18	k	k	NOUN
ejpam-2979	4	19	,	,	PUNCT
ejpam-2979	4	20	we	we	PRON
ejpam-2979	4	21	derive	derive	VERB
ejpam-2979	4	22	some	some	DET
ejpam-2979	4	23	combinatorial	combinatorial	ADJ
ejpam-2979	4	24	identities	identity	NOUN
ejpam-2979	4	25	for	for	ADP
ejpam-2979	4	26	the	the	DET
ejpam-2979	4	27	sequence	sequence	NOUN
ejpam-2979	4	28	{	{	PUNCT
ejpam-2979	4	29	gkn	gkn	NOUN
ejpam-2979	4	30	}	}	PUNCT
ejpam-2979	4	31	.	.	PUNCT
ejpam-2979	5	1	2010	2010	NUM
ejpam-2979	5	2	mathematics	mathematic	NOUN
ejpam-2979	5	3	subject	subject	NOUN
ejpam-2979	5	4	classifications	classification	NOUN
ejpam-2979	5	5	:	:	PUNCT
ejpam-2979	5	6	11b39	11b39	NUM
ejpam-2979	5	7	,	,	PUNCT
ejpam-2979	5	8	05a10	05a10	NOUN
ejpam-2979	5	9	,	,	PUNCT
ejpam-2979	5	10	05a15	05a15	NUM
ejpam-2979	5	11	,	,	PUNCT
ejpam-2979	5	12	05a19	05a19	VERB
ejpam-2979	5	13	key	key	ADJ
ejpam-2979	5	14	words	word	NOUN
ejpam-2979	5	15	and	and	CCONJ
ejpam-2979	5	16	phrases	phrase	NOUN
ejpam-2979	5	17	:	:	PUNCT
ejpam-2979	5	18	binomial	binomial	ADJ
ejpam-2979	5	19	sums	sum	NOUN
ejpam-2979	5	20	,	,	PUNCT
ejpam-2979	5	21	generalized	generalized	ADJ
ejpam-2979	5	22	fibonacci	fibonacci	NOUN
ejpam-2979	5	23	numbers	number	NOUN
ejpam-2979	5	24	,	,	PUNCT
ejpam-2979	5	25	recurrence	recurrence	NOUN
ejpam-2979	5	26	relation	relation	NOUN
ejpam-2979	5	27	1	1	NUM
ejpam-2979	5	28	.	.	PUNCT
ejpam-2979	6	1	introduction	introduction	NOUN
ejpam-2979	6	2	matrix	matrix	NOUN
ejpam-2979	6	3	methods	method	NOUN
ejpam-2979	6	4	are	be	AUX
ejpam-2979	6	5	very	very	ADV
ejpam-2979	6	6	convenient	convenient	ADJ
ejpam-2979	6	7	for	for	ADP
ejpam-2979	6	8	deriving	derive	VERB
ejpam-2979	6	9	certain	certain	ADJ
ejpam-2979	6	10	of	of	ADP
ejpam-2979	6	11	linear	linear	ADJ
ejpam-2979	6	12	recurrence	recurrence	NOUN
ejpam-2979	6	13	sequences	sequence	NOUN
ejpam-2979	6	14	.	.	PUNCT
ejpam-2979	7	1	some	some	DET
ejpam-2979	7	2	authors	author	NOUN
ejpam-2979	7	3	have	have	AUX
ejpam-2979	7	4	used	use	VERB
ejpam-2979	7	5	matrix	matrix	NOUN
ejpam-2979	7	6	methods	method	NOUN
ejpam-2979	7	7	of	of	ADP
ejpam-2979	7	8	other	other	ADJ
ejpam-2979	7	9	methods	method	NOUN
ejpam-2979	7	10	to	to	PART
ejpam-2979	7	11	derive	derive	VERB
ejpam-2979	7	12	some	some	DET
ejpam-2979	7	13	identities	identity	NOUN
ejpam-2979	7	14	,	,	PUNCT
ejpam-2979	7	15	combinatorial	combinatorial	ADJ
ejpam-2979	7	16	representations	representation	NOUN
ejpam-2979	7	17	of	of	ADP
ejpam-2979	7	18	linear	linear	ADJ
ejpam-2979	7	19	recurrence	recurrence	NOUN
ejpam-2979	7	20	relations	relation	NOUN
ejpam-2979	7	21	etc[3	etc[3	PROPN
ejpam-2979	7	22	,	,	PUNCT
ejpam-2979	7	23	6	6	NUM
ejpam-2979	7	24	,	,	PUNCT
ejpam-2979	7	25	10	10	NUM
ejpam-2979	7	26	,	,	PUNCT
ejpam-2979	7	27	13	13	NUM
ejpam-2979	7	28	,	,	PUNCT
ejpam-2979	7	29	14	14	NUM
ejpam-2979	7	30	,	,	PUNCT
ejpam-2979	7	31	15	15	NUM
ejpam-2979	7	32	,	,	PUNCT
ejpam-2979	7	33	16	16	NUM
ejpam-2979	7	34	,	,	PUNCT
ejpam-2979	7	35	8	8	NUM
ejpam-2979	7	36	,	,	PUNCT
ejpam-2979	7	37	9	9	NUM
ejpam-2979	7	38	]	]	PUNCT
ejpam-2979	7	39	.	.	PUNCT
ejpam-2979	8	1	in	in	ADP
ejpam-2979	8	2	[	[	X
ejpam-2979	8	3	13	13	NUM
ejpam-2979	8	4	]	]	PUNCT
ejpam-2979	8	5	,	,	PUNCT
ejpam-2979	8	6	the	the	DET
ejpam-2979	8	7	author	author	NOUN
ejpam-2979	8	8	gives	give	VERB
ejpam-2979	8	9	a	a	DET
ejpam-2979	8	10	new	new	ADJ
ejpam-2979	8	11	formula	formula	NOUN
ejpam-2979	8	12	for	for	ADP
ejpam-2979	8	13	the	the	DET
ejpam-2979	8	14	nth	nth	NOUN
ejpam-2979	8	15	power	power	NOUN
ejpam-2979	8	16	of	of	ADP
ejpam-2979	8	17	an	an	DET
ejpam-2979	8	18	arbitrary	arbitrary	ADJ
ejpam-2979	8	19	2×	2×	NUM
ejpam-2979	8	20	2	2	NUM
ejpam-2979	8	21	matrix	matrix	NOUN
ejpam-2979	8	22	and	and	CCONJ
ejpam-2979	8	23	derive	derive	VERB
ejpam-2979	8	24	various	various	ADJ
ejpam-2979	8	25	matrix	matrix	NOUN
ejpam-2979	8	26	identities	identity	NOUN
ejpam-2979	8	27	and	and	CCONJ
ejpam-2979	8	28	formulae	formulae	NOUN
ejpam-2979	8	29	for	for	ADP
ejpam-2979	8	30	the	the	DET
ejpam-2979	8	31	nth	nth	NOUN
ejpam-2979	8	32	power	power	NOUN
ejpam-2979	8	33	of	of	ADP
ejpam-2979	8	34	particular	particular	ADJ
ejpam-2979	8	35	matrices	matrix	NOUN
ejpam-2979	8	36	to	to	PART
ejpam-2979	8	37	obtain	obtain	VERB
ejpam-2979	8	38	various	various	ADJ
ejpam-2979	8	39	combinatorial	combinatorial	ADJ
ejpam-2979	8	40	identities	identity	NOUN
ejpam-2979	8	41	.	.	PUNCT
ejpam-2979	9	1	the	the	DET
ejpam-2979	9	2	generalized	generalized	ADJ
ejpam-2979	9	3	second	second	ADJ
ejpam-2979	9	4	order	order	NOUN
ejpam-2979	9	5	sequences	sequence	NOUN
ejpam-2979	9	6	{	{	PUNCT
ejpam-2979	9	7	un	un	PROPN
ejpam-2979	9	8	}	}	PUNCT
ejpam-2979	9	9	and	and	CCONJ
ejpam-2979	9	10	{	{	PUNCT
ejpam-2979	9	11	vn	vn	NOUN
ejpam-2979	9	12	}	}	PUNCT
ejpam-2979	9	13	,	,	PUNCT
ejpam-2979	9	14	are	be	AUX
ejpam-2979	9	15	defined	define	VERB
ejpam-2979	9	16	for	for	ADP
ejpam-2979	9	17	n	n	X
ejpam-2979	9	18	>	>	SYM
ejpam-2979	9	19	0	0	NUM
ejpam-2979	9	20	and	and	CCONJ
ejpam-2979	9	21	nonzero	nonzero	NOUN
ejpam-2979	9	22	integer	integer	NOUN
ejpam-2979	9	23	numbers	number	NOUN
ejpam-2979	9	24	p	p	NOUN
ejpam-2979	9	25	,	,	PUNCT
ejpam-2979	9	26	q	q	NOUN
ejpam-2979	9	27	by	by	ADP
ejpam-2979	9	28	un+1	un+1	NOUN
ejpam-2979	9	29	=	=	SYM
ejpam-2979	9	30	pun	pun	NOUN
ejpam-2979	9	31	+	+	CCONJ
ejpam-2979	9	32	qun−1	qun−1	PROPN
ejpam-2979	9	33	and	and	CCONJ
ejpam-2979	9	34	vn+1	vn+1	NOUN
ejpam-2979	9	35	=	=	SYM
ejpam-2979	9	36	pvn	pvn	NOUN
ejpam-2979	9	37	+	+	CCONJ
ejpam-2979	9	38	qvn−1	qvn−1	PROPN
ejpam-2979	9	39	in	in	ADP
ejpam-2979	9	40	which	which	PRON
ejpam-2979	9	41	u0	u0	ADJ
ejpam-2979	9	42	=	=	SYM
ejpam-2979	9	43	0	0	NUM
ejpam-2979	9	44	,	,	PUNCT
ejpam-2979	9	45	u1	u1	NOUN
ejpam-2979	9	46	=	=	SYM
ejpam-2979	9	47	1	1	NUM
ejpam-2979	9	48	and	and	CCONJ
ejpam-2979	9	49	v0	v0	NOUN
ejpam-2979	9	50	=	=	SYM
ejpam-2979	9	51	2	2	NUM
ejpam-2979	9	52	,	,	PUNCT
ejpam-2979	9	53	v1	v1	NOUN
ejpam-2979	9	54	=	=	SYM
ejpam-2979	9	55	p	p	NOUN
ejpam-2979	9	56	,	,	PUNCT
ejpam-2979	9	57	respectively	respectively	ADV
ejpam-2979	9	58	.	.	PUNCT
ejpam-2979	10	1	when	when	SCONJ
ejpam-2979	10	2	p	p	NOUN
ejpam-2979	10	3	=	=	X
ejpam-2979	10	4	q	q	NOUN
ejpam-2979	10	5	=	=	SYM
ejpam-2979	10	6	1	1	NUM
ejpam-2979	10	7	,	,	PUNCT
ejpam-2979	10	8	un	un	PROPN
ejpam-2979	10	9	=	=	PROPN
ejpam-2979	10	10	fn	fn	PROPN
ejpam-2979	10	11	(	(	PUNCT
ejpam-2979	10	12	the	the	DET
ejpam-2979	10	13	nth	nth	PROPN
ejpam-2979	10	14	fibonacci	fibonacci	NOUN
ejpam-2979	10	15	number	number	NOUN
ejpam-2979	10	16	)	)	PUNCT
ejpam-2979	10	17	and	and	CCONJ
ejpam-2979	10	18	vn	vn	X
ejpam-2979	10	19	=	=	SYM
ejpam-2979	10	20	ln	ln	PROPN
ejpam-2979	10	21	(	(	PUNCT
ejpam-2979	10	22	the	the	DET
ejpam-2979	10	23	nth	nth	PROPN
ejpam-2979	10	24	lucas	lucas	PROPN
ejpam-2979	10	25	number	number	PROPN
ejpam-2979	10	26	)	)	PUNCT
ejpam-2979	10	27	.	.	PUNCT
ejpam-2979	11	1	if	if	SCONJ
ejpam-2979	11	2	α	α	PROPN
ejpam-2979	11	3	and	and	CCONJ
ejpam-2979	11	4	β	β	X
ejpam-2979	11	5	are	be	AUX
ejpam-2979	11	6	the	the	DET
ejpam-2979	11	7	roots	root	NOUN
ejpam-2979	11	8	of	of	ADP
ejpam-2979	11	9	equation	equation	NOUN
ejpam-2979	11	10	x2−px−q	x2−px−q	PUNCT
ejpam-2979	12	1	=	=	SYM
ejpam-2979	12	2	0	0	PROPN
ejpam-2979	12	3	,	,	PUNCT
ejpam-2979	12	4	the	the	DET
ejpam-2979	12	5	binet	binet	NOUN
ejpam-2979	12	6	formulae	formulae	NOUN
ejpam-2979	12	7	of	of	ADP
ejpam-2979	12	8	the	the	DET
ejpam-2979	12	9	sequences	sequence	NOUN
ejpam-2979	12	10	{	{	PUNCT
ejpam-2979	12	11	un	un	PROPN
ejpam-2979	12	12	}	}	PUNCT
ejpam-2979	12	13	and	and	CCONJ
ejpam-2979	12	14	{	{	PUNCT
ejpam-2979	12	15	vn	vn	NOUN
ejpam-2979	12	16	}	}	PUNCT
ejpam-2979	12	17	have	have	VERB
ejpam-2979	12	18	the	the	DET
ejpam-2979	12	19	form	form	NOUN
ejpam-2979	12	20	un	un	PROPN
ejpam-2979	12	21	=	=	NOUN
ejpam-2979	12	22	αn	αn	NOUN
ejpam-2979	12	23	−	−	PROPN
ejpam-2979	13	1	βn	βn	NOUN
ejpam-2979	13	2	α−	α−	ADP
ejpam-2979	13	3	β	β	X
ejpam-2979	13	4	and	and	CCONJ
ejpam-2979	13	5	vn	vn	X
ejpam-2979	13	6	=	=	PUNCT
ejpam-2979	13	7	αn	αn	PROPN
ejpam-2979	14	1	+	+	CCONJ
ejpam-2979	14	2	βn	βn	ADJ
ejpam-2979	14	3	,	,	PUNCT
ejpam-2979	14	4	∗corresponding	∗corresponde	VERB
ejpam-2979	14	5	author	author	NOUN
ejpam-2979	14	6	.	.	PUNCT
ejpam-2979	15	1	email	email	NOUN
ejpam-2979	15	2	addresses	address	NOUN
ejpam-2979	15	3	:	:	PUNCT
ejpam-2979	15	4	neseomur@kocaeli.edu.tr	neseomur@kocaeli.edu.tr	ADV
ejpam-2979	15	5	(	(	PUNCT
ejpam-2979	15	6	n.	n.	NOUN
ejpam-2979	15	7	ömür	ömür	NOUN
ejpam-2979	15	8	,	,	PUNCT
ejpam-2979	15	9	)	)	PUNCT
ejpam-2979	15	10	cemileduygusener@gmail.com	cemileduygusener@gmail.com	X
ejpam-2979	15	11	(	(	PUNCT
ejpam-2979	15	12	c.d.şener	c.d.şener	NOUN
ejpam-2979	15	13	)	)	PUNCT
ejpam-2979	15	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2979	16	1	506	506	NUM
ejpam-2979	16	2	c	c	NOUN
ejpam-2979	16	3	©	©	PROPN
ejpam-2979	16	4	2017	2017	NUM
ejpam-2979	16	5	ejpam	ejpam	VERB
ejpam-2979	16	6	all	all	DET
ejpam-2979	16	7	rights	right	NOUN
ejpam-2979	16	8	reserved	reserve	VERB
ejpam-2979	16	9	.	.	PUNCT
ejpam-2979	17	1	n.	n.	PROPN
ejpam-2979	17	2	ömür	ömür	PROPN
ejpam-2979	17	3	,	,	PUNCT
ejpam-2979	17	4	c.	c.	PROPN
ejpam-2979	17	5	d.	d.	PROPN
ejpam-2979	17	6	şener	şener	PROPN
ejpam-2979	17	7	/	/	SYM
ejpam-2979	17	8	eur	eur	PROPN
ejpam-2979	17	9	.	.	PUNCT
ejpam-2979	18	1	j.	j.	PROPN
ejpam-2979	18	2	pure	pure	PROPN
ejpam-2979	18	3	appl	appl	PROPN
ejpam-2979	18	4	.	.	PROPN
ejpam-2979	18	5	math	math	PROPN
ejpam-2979	18	6	,	,	PUNCT
ejpam-2979	18	7	10	10	NUM
ejpam-2979	18	8	(	(	PUNCT
ejpam-2979	18	9	3	3	NUM
ejpam-2979	18	10	)	)	PUNCT
ejpam-2979	18	11	(	(	PUNCT
ejpam-2979	18	12	2017	2017	NUM
ejpam-2979	18	13	)	)	PUNCT
ejpam-2979	18	14	,	,	PUNCT
ejpam-2979	18	15	506	506	NUM
ejpam-2979	18	16	-	-	SYM
ejpam-2979	18	17	515	515	NUM
ejpam-2979	18	18	507	507	NUM
ejpam-2979	18	19	respectively	respectively	ADV
ejpam-2979	18	20	.	.	PUNCT
ejpam-2979	19	1	from	from	ADP
ejpam-2979	19	2	[	[	X
ejpam-2979	19	3	7	7	NUM
ejpam-2979	19	4	]	]	PUNCT
ejpam-2979	19	5	,	,	PUNCT
ejpam-2979	19	6	e.	e.	PROPN
ejpam-2979	19	7	kılıç	kılıç	PROPN
ejpam-2979	19	8	and	and	CCONJ
ejpam-2979	19	9	p.	p.	PROPN
ejpam-2979	19	10	stanica	stanica	PROPN
ejpam-2979	19	11	derived	derive	VERB
ejpam-2979	19	12	the	the	DET
ejpam-2979	19	13	following	follow	VERB
ejpam-2979	19	14	recurrence	recurrence	NOUN
ejpam-2979	19	15	relations	relation	NOUN
ejpam-2979	19	16	for	for	ADP
ejpam-2979	19	17	the	the	DET
ejpam-2979	19	18	sequences	sequence	NOUN
ejpam-2979	19	19	{	{	PUNCT
ejpam-2979	19	20	ukn	ukn	NOUN
ejpam-2979	19	21	}	}	PUNCT
ejpam-2979	19	22	and	and	CCONJ
ejpam-2979	19	23	{	{	PUNCT
ejpam-2979	19	24	vkn	vkn	NOUN
ejpam-2979	19	25	}	}	PUNCT
ejpam-2979	19	26	for	for	ADP
ejpam-2979	19	27	k	k	PROPN
ejpam-2979	19	28	≥	≥	PROPN
ejpam-2979	19	29	0	0	NUM
ejpam-2979	19	30	,	,	PUNCT
ejpam-2979	19	31	n	n	CCONJ
ejpam-2979	19	32	>	>	X
ejpam-2979	19	33	0	0	X
ejpam-2979	19	34	.	.	PUNCT
ejpam-2979	20	1	it	it	PRON
ejpam-2979	20	2	is	be	AUX
ejpam-2979	20	3	clearly	clearly	ADV
ejpam-2979	20	4	that	that	PRON
ejpam-2979	20	5	uk(n+1	uk(n+1	NOUN
ejpam-2979	20	6	)	)	PUNCT
ejpam-2979	21	1	=	=	SYM
ejpam-2979	21	2	vkukn	vkukn	NOUN
ejpam-2979	21	3	+	+	CCONJ
ejpam-2979	21	4	(	(	PUNCT
ejpam-2979	21	5	−1)k+1	−1)k+1	VERB
ejpam-2979	21	6	qkuk(n−1	qkuk(n−1	PROPN
ejpam-2979	21	7	)	)	PUNCT
ejpam-2979	21	8	and	and	CCONJ
ejpam-2979	21	9	vk(n+1	vk(n+1	NOUN
ejpam-2979	21	10	)	)	PUNCT
ejpam-2979	21	11	=	=	VERB
ejpam-2979	21	12	vkvkn	vkvkn	NOUN
ejpam-2979	21	13	+	+	CCONJ
ejpam-2979	21	14	(	(	PUNCT
ejpam-2979	21	15	−1)k+1	−1)k+1	VERB
ejpam-2979	21	16	qkvk(n−1	qkvk(n−1	PROPN
ejpam-2979	21	17	)	)	PUNCT
ejpam-2979	21	18	,	,	PUNCT
ejpam-2979	21	19	where	where	SCONJ
ejpam-2979	21	20	the	the	DET
ejpam-2979	21	21	initial	initial	ADJ
ejpam-2979	21	22	conditions	condition	NOUN
ejpam-2979	21	23	of	of	ADP
ejpam-2979	21	24	the	the	DET
ejpam-2979	21	25	sequences	sequence	NOUN
ejpam-2979	21	26	{	{	PUNCT
ejpam-2979	21	27	ukn	ukn	NOUN
ejpam-2979	21	28	}	}	PUNCT
ejpam-2979	21	29	and	and	CCONJ
ejpam-2979	21	30	{	{	PUNCT
ejpam-2979	21	31	vkn	vkn	NOUN
ejpam-2979	21	32	}	}	PUNCT
ejpam-2979	21	33	are	be	AUX
ejpam-2979	21	34	0	0	NUM
ejpam-2979	21	35	,	,	PUNCT
ejpam-2979	21	36	uk	uk	PROPN
ejpam-2979	21	37	,	,	PUNCT
ejpam-2979	21	38	and	and	CCONJ
ejpam-2979	21	39	2	2	NUM
ejpam-2979	21	40	,	,	PUNCT
ejpam-2979	21	41	vk	vk	NOUN
ejpam-2979	21	42	,	,	PUNCT
ejpam-2979	21	43	respectively	respectively	ADV
ejpam-2979	21	44	.	.	PUNCT
ejpam-2979	22	1	the	the	DET
ejpam-2979	22	2	binet	binet	NOUN
ejpam-2979	22	3	formulae	formulae	NOUN
ejpam-2979	22	4	of	of	ADP
ejpam-2979	22	5	the	the	DET
ejpam-2979	22	6	sequences	sequence	NOUN
ejpam-2979	22	7	{	{	PUNCT
ejpam-2979	22	8	ukn	ukn	NOUN
ejpam-2979	22	9	}	}	PUNCT
ejpam-2979	22	10	and	and	CCONJ
ejpam-2979	22	11	{	{	PUNCT
ejpam-2979	22	12	vkn	vkn	NOUN
ejpam-2979	22	13	}	}	PUNCT
ejpam-2979	22	14	are	be	AUX
ejpam-2979	22	15	given	give	VERB
ejpam-2979	22	16	by	by	ADP
ejpam-2979	22	17	ukn	ukn	PROPN
ejpam-2979	22	18	=	=	SYM
ejpam-2979	22	19	αkn	αkn	NOUN
ejpam-2979	22	20	−	−	NOUN
ejpam-2979	22	21	βkn	βkn	NOUN
ejpam-2979	22	22	α−	α−	ADP
ejpam-2979	22	23	β	β	X
ejpam-2979	22	24	and	and	CCONJ
ejpam-2979	22	25	vkn	vkn	NOUN
ejpam-2979	22	26	=	=	SYM
ejpam-2979	22	27	αkn	αkn	NOUN
ejpam-2979	22	28	+	+	CCONJ
ejpam-2979	22	29	βkn	βkn	NOUN
ejpam-2979	22	30	,	,	PUNCT
ejpam-2979	22	31	respectively	respectively	ADV
ejpam-2979	22	32	.	.	PUNCT
ejpam-2979	23	1	from	from	ADP
ejpam-2979	23	2	the	the	DET
ejpam-2979	23	3	binet	binet	NOUN
ejpam-2979	23	4	formulas	formula	NOUN
ejpam-2979	23	5	,	,	PUNCT
ejpam-2979	23	6	one	one	PRON
ejpam-2979	23	7	can	can	AUX
ejpam-2979	23	8	see	see	VERB
ejpam-2979	23	9	that	that	DET
ejpam-2979	23	10	u−kn	u−kn	NOUN
ejpam-2979	23	11	=	=	PRON
ejpam-2979	23	12	(	(	PUNCT
ejpam-2979	23	13	−1)kn+1	−1)kn+1	X
ejpam-2979	23	14	ukn	ukn	PROPN
ejpam-2979	23	15	and	and	CCONJ
ejpam-2979	23	16	u2kn	u2kn	ADV
ejpam-2979	23	17	=	=	SYM
ejpam-2979	23	18	uknvkn	uknvkn	NOUN
ejpam-2979	23	19	.	.	PUNCT
ejpam-2979	24	1	in	in	ADP
ejpam-2979	24	2	[	[	X
ejpam-2979	24	3	1	1	NUM
ejpam-2979	24	4	]	]	PUNCT
ejpam-2979	24	5	and	and	CCONJ
ejpam-2979	24	6	[	[	X
ejpam-2979	24	7	2	2	NUM
ejpam-2979	24	8	]	]	PUNCT
ejpam-2979	24	9	,	,	PUNCT
ejpam-2979	24	10	the	the	DET
ejpam-2979	24	11	authors	author	NOUN
ejpam-2979	24	12	obtained	obtain	VERB
ejpam-2979	24	13	some	some	DET
ejpam-2979	24	14	new	new	ADJ
ejpam-2979	24	15	identities	identity	NOUN
ejpam-2979	24	16	for	for	ADP
ejpam-2979	24	17	the	the	DET
ejpam-2979	24	18	sequence	sequence	NOUN
ejpam-2979	24	19	{	{	PUNCT
ejpam-2979	24	20	un	un	PROPN
ejpam-2979	24	21	}	}	PUNCT
ejpam-2979	24	22	.	.	PUNCT
ejpam-2979	25	1	for	for	ADP
ejpam-2979	25	2	example	example	NOUN
ejpam-2979	25	3	,	,	PUNCT
ejpam-2979	25	4	for	for	ADP
ejpam-2979	25	5	n	n	PRON
ejpam-2979	25	6	≥	≥	NUM
ejpam-2979	25	7	1	1	NUM
ejpam-2979	25	8	,	,	PUNCT
ejpam-2979	25	9	n∑	n∑	DET
ejpam-2979	25	10	k=0	k=0	PROPN
ejpam-2979	25	11	(	(	PUNCT
ejpam-2979	25	12	n	n	X
ejpam-2979	25	13	k	k	NOUN
ejpam-2979	25	14	)	)	PUNCT
ejpam-2979	25	15	(	(	PUNCT
ejpam-2979	25	16	α	α	X
ejpam-2979	25	17	q	q	NOUN
ejpam-2979	25	18	)	)	PUNCT
ejpam-2979	25	19	k	k	PROPN
ejpam-2979	25	20	uk	uk	PROPN
ejpam-2979	25	21	=	=	PROPN
ejpam-2979	25	22	α	α	PROPN
ejpam-2979	25	23	q	q	PROPN
ejpam-2979	25	24	(	(	PUNCT
ejpam-2979	25	25	pα	pα	INTJ
ejpam-2979	25	26	q	q	NOUN
ejpam-2979	26	1	+	+	NUM
ejpam-2979	26	2	2	2	NUM
ejpam-2979	26	3	)	)	PUNCT
ejpam-2979	26	4	n−1	n−1	PROPN
ejpam-2979	26	5	,	,	PUNCT
ejpam-2979	26	6	and	and	CCONJ
ejpam-2979	26	7	n∑	n∑	PROPN
ejpam-2979	26	8	k=0	k=0	PROPN
ejpam-2979	26	9	(	(	PUNCT
ejpam-2979	26	10	n	n	X
ejpam-2979	26	11	k	k	NOUN
ejpam-2979	26	12	)	)	PUNCT
ejpam-2979	26	13	(	(	PUNCT
ejpam-2979	26	14	β	β	X
ejpam-2979	26	15	q	q	NOUN
ejpam-2979	26	16	)	)	PUNCT
ejpam-2979	26	17	k	k	PROPN
ejpam-2979	26	18	uk	uk	PROPN
ejpam-2979	26	19	=	=	PUNCT
ejpam-2979	26	20	β	β	X
ejpam-2979	26	21	q	q	X
ejpam-2979	26	22	(	(	PUNCT
ejpam-2979	26	23	pβ	pβ	ADV
ejpam-2979	26	24	q	q	X
ejpam-2979	26	25	+	+	NUM
ejpam-2979	26	26	2	2	NUM
ejpam-2979	26	27	)	)	PUNCT
ejpam-2979	26	28	n−1	n−1	PROPN
ejpam-2979	26	29	.	.	PUNCT
ejpam-2979	27	1	let	let	VERB
ejpam-2979	27	2	{	{	PUNCT
ejpam-2979	27	3	ak	ak	VERB
ejpam-2979	27	4	}	}	PUNCT
ejpam-2979	27	5	and	and	CCONJ
ejpam-2979	27	6	{	{	PUNCT
ejpam-2979	27	7	bk	bk	AUX
ejpam-2979	27	8	}	}	PUNCT
ejpam-2979	27	9	be	be	AUX
ejpam-2979	27	10	sequences	sequence	NOUN
ejpam-2979	27	11	with	with	ADP
ejpam-2979	27	12	the	the	DET
ejpam-2979	27	13	property	property	NOUN
ejpam-2979	27	14	that	that	PRON
ejpam-2979	27	15	ak	ak	PROPN
ejpam-2979	27	16	is	be	AUX
ejpam-2979	27	17	the	the	DET
ejpam-2979	27	18	finite	finite	ADJ
ejpam-2979	27	19	difference	difference	NOUN
ejpam-2979	27	20	of	of	ADP
ejpam-2979	27	21	bk	bk	NOUN
ejpam-2979	27	22	,	,	PUNCT
ejpam-2979	27	23	that	that	ADV
ejpam-2979	27	24	is	is	ADV
ejpam-2979	27	25	,	,	PUNCT
ejpam-2979	27	26	ak	ak	PROPN
ejpam-2979	27	27	=	=	PROPN
ejpam-2979	27	28	∆bk	∆bk	NOUN
ejpam-2979	27	29	:	:	PUNCT
ejpam-2979	27	30	=	=	SYM
ejpam-2979	27	31	bk+1	bk+1	NOUN
ejpam-2979	27	32	−	−	NOUN
ejpam-2979	27	33	bk	bk	VERB
ejpam-2979	27	34	,	,	PUNCT
ejpam-2979	27	35	for	for	ADP
ejpam-2979	27	36	k	k	PROPN
ejpam-2979	27	37	≥	≥	PROPN
ejpam-2979	27	38	0	0	NUM
ejpam-2979	27	39	.	.	PUNCT
ejpam-2979	28	1	we	we	PRON
ejpam-2979	28	2	take	take	VERB
ejpam-2979	28	3	gn	gn	PROPN
ejpam-2979	28	4	=	=	PUNCT
ejpam-2979	28	5	n∑	n∑	PROPN
ejpam-2979	28	6	k=0	k=0	PROPN
ejpam-2979	28	7	(	(	PUNCT
ejpam-2979	28	8	n	n	X
ejpam-2979	28	9	k	k	X
ejpam-2979	28	10	)	)	PUNCT
ejpam-2979	28	11	ak	ak	PROPN
ejpam-2979	28	12	and	and	CCONJ
ejpam-2979	28	13	hn	hn	PROPN
ejpam-2979	28	14	=	=	PROPN
ejpam-2979	28	15	n∑	n∑	PROPN
ejpam-2979	28	16	k=0	k=0	PROPN
ejpam-2979	28	17	(	(	PUNCT
ejpam-2979	28	18	n	n	X
ejpam-2979	28	19	k	k	PROPN
ejpam-2979	28	20	)	)	PUNCT
ejpam-2979	28	21	bk	bk	PROPN
ejpam-2979	28	22	.	.	PUNCT
ejpam-2979	29	1	(	(	PUNCT
ejpam-2979	29	2	1	1	X
ejpam-2979	29	3	)	)	PUNCT
ejpam-2979	29	4	in	in	ADP
ejpam-2979	29	5	[	[	X
ejpam-2979	29	6	11	11	NUM
ejpam-2979	29	7	]	]	PUNCT
ejpam-2979	29	8	,	,	PUNCT
ejpam-2979	29	9	komatsu	komatsu	NOUN
ejpam-2979	29	10	obtained	obtain	VERB
ejpam-2979	29	11	several	several	ADJ
ejpam-2979	29	12	sequences	sequence	NOUN
ejpam-2979	29	13	of	of	ADP
ejpam-2979	29	14	binomial	binomial	ADJ
ejpam-2979	29	15	sums	sum	NOUN
ejpam-2979	29	16	of	of	ADP
ejpam-2979	29	17	generalized	generalized	ADJ
ejpam-2979	29	18	fibonacci	fibonacci	NOUN
ejpam-2979	29	19	numbers	number	NOUN
ejpam-2979	29	20	.	.	PUNCT
ejpam-2979	30	1	for	for	ADP
ejpam-2979	30	2	example	example	NOUN
ejpam-2979	30	3	,	,	PUNCT
ejpam-2979	30	4	n∑	n∑	PROPN
ejpam-2979	30	5	k=0	k=0	PROPN
ejpam-2979	30	6	(	(	PUNCT
ejpam-2979	30	7	n	n	CCONJ
ejpam-2979	30	8	k	k	NOUN
ejpam-2979	30	9	)	)	PUNCT
ejpam-2979	30	10	ckuk	ckuk	NOUN
ejpam-2979	30	11	=	=	SYM
ejpam-2979	30	12	rn	rn	PROPN
ejpam-2979	30	13	(	(	PUNCT
ejpam-2979	30	14	n	n	CCONJ
ejpam-2979	30	15	≥	≥	NOUN
ejpam-2979	30	16	0	0	NUM
ejpam-2979	30	17	)	)	PUNCT
ejpam-2979	30	18	satisfies	satisfy	VERB
ejpam-2979	30	19	the	the	DET
ejpam-2979	30	20	recurrence	recurrence	PROPN
ejpam-2979	30	21	relation	relation	PROPN
ejpam-2979	30	22	rn	rn	PROPN
ejpam-2979	30	23	=	=	PROPN
ejpam-2979	30	24	(	(	PUNCT
ejpam-2979	30	25	ac+	ac+	NOUN
ejpam-2979	30	26	2	2	NUM
ejpam-2979	30	27	)	)	PUNCT
ejpam-2979	30	28	rn−1	rn−1	NOUN
ejpam-2979	30	29	+	+	CCONJ
ejpam-2979	30	30	(	(	PUNCT
ejpam-2979	30	31	bc2	bc2	VERB
ejpam-2979	30	32	−	−	PUNCT
ejpam-2979	30	33	ac−	ac−	PROPN
ejpam-2979	30	34	1	1	NUM
ejpam-2979	30	35	)	)	PUNCT
ejpam-2979	30	36	rn−2	rn−2	PROPN
ejpam-2979	30	37	(	(	PUNCT
ejpam-2979	30	38	n	n	CCONJ
ejpam-2979	30	39	≥	≥	NOUN
ejpam-2979	30	40	2	2	NUM
ejpam-2979	30	41	)	)	PUNCT
ejpam-2979	30	42	with	with	ADP
ejpam-2979	30	43	r0	r0	NOUN
ejpam-2979	30	44	=	=	SYM
ejpam-2979	30	45	0	0	NUM
ejpam-2979	30	46	,	,	PUNCT
ejpam-2979	30	47	r1	r1	NOUN
ejpam-2979	30	48	=	=	PUNCT
ejpam-2979	30	49	c	c	PROPN
ejpam-2979	30	50	and	and	CCONJ
ejpam-2979	30	51	n∑	n∑	PROPN
ejpam-2979	30	52	k=0	k=0	PROPN
ejpam-2979	30	53	(	(	PUNCT
ejpam-2979	30	54	n	n	X
ejpam-2979	30	55	k	k	NOUN
ejpam-2979	30	56	)	)	PUNCT
ejpam-2979	30	57	cn−kdkuk	cn−kdkuk	NOUN
ejpam-2979	30	58	=	=	SYM
ejpam-2979	30	59	λn	λn	NOUN
ejpam-2979	30	60	(	(	PUNCT
ejpam-2979	30	61	n	n	CCONJ
ejpam-2979	30	62	≥	≥	NOUN
ejpam-2979	30	63	0	0	NUM
ejpam-2979	30	64	)	)	PUNCT
ejpam-2979	30	65	satisfies	satisfy	VERB
ejpam-2979	30	66	the	the	DET
ejpam-2979	30	67	recurrence	recurrence	NOUN
ejpam-2979	30	68	relation	relation	NOUN
ejpam-2979	30	69	λn	λn	NOUN
ejpam-2979	30	70	=	=	PUNCT
ejpam-2979	30	71	(	(	PUNCT
ejpam-2979	30	72	ad+	ad+	X
ejpam-2979	30	73	2c)λn−1	2c)λn−1	ADJ
ejpam-2979	30	74	+	+	CCONJ
ejpam-2979	30	75	(	(	PUNCT
ejpam-2979	30	76	bd2	bd2	NOUN
ejpam-2979	30	77	−	−	PROPN
ejpam-2979	30	78	acd−	acd−	PROPN
ejpam-2979	30	79	c2	c2	PROPN
ejpam-2979	30	80	)	)	PUNCT
ejpam-2979	31	1	λn−2	λn−2	PROPN
ejpam-2979	31	2	(	(	PUNCT
ejpam-2979	31	3	n	n	CCONJ
ejpam-2979	31	4	≥	≥	NOUN
ejpam-2979	31	5	2	2	NUM
ejpam-2979	31	6	)	)	PUNCT
ejpam-2979	31	7	with	with	ADP
ejpam-2979	31	8	initial	initial	ADJ
ejpam-2979	31	9	conditions	condition	NOUN
ejpam-2979	31	10	λ0	λ0	NOUN
ejpam-2979	31	11	=	=	SYM
ejpam-2979	31	12	0	0	NUM
ejpam-2979	31	13	and	and	CCONJ
ejpam-2979	31	14	λ1	λ1	PROPN
ejpam-2979	31	15	=	=	SYM
ejpam-2979	31	16	d	d	PROPN
ejpam-2979	31	17	,	,	PUNCT
ejpam-2979	31	18	where	where	SCONJ
ejpam-2979	31	19	c	c	X
ejpam-2979	31	20	,	,	PUNCT
ejpam-2979	31	21	d	d	X
ejpam-2979	31	22	are	be	AUX
ejpam-2979	31	23	nonzero	nonzero	ADJ
ejpam-2979	31	24	real	real	ADJ
ejpam-2979	31	25	numbers	number	NOUN
ejpam-2979	31	26	.	.	PUNCT
ejpam-2979	32	1	n.	n.	PROPN
ejpam-2979	32	2	ömür	ömür	PROPN
ejpam-2979	32	3	,	,	PUNCT
ejpam-2979	32	4	c.	c.	PROPN
ejpam-2979	32	5	d.	d.	PROPN
ejpam-2979	32	6	şener	şener	PROPN
ejpam-2979	32	7	/	/	SYM
ejpam-2979	32	8	eur	eur	PROPN
ejpam-2979	32	9	.	.	PUNCT
ejpam-2979	33	1	j.	j.	PROPN
ejpam-2979	33	2	pure	pure	PROPN
ejpam-2979	33	3	appl	appl	PROPN
ejpam-2979	33	4	.	.	PROPN
ejpam-2979	33	5	math	math	PROPN
ejpam-2979	33	6	,	,	PUNCT
ejpam-2979	33	7	10	10	NUM
ejpam-2979	33	8	(	(	PUNCT
ejpam-2979	33	9	3	3	NUM
ejpam-2979	33	10	)	)	PUNCT
ejpam-2979	33	11	(	(	PUNCT
ejpam-2979	33	12	2017	2017	NUM
ejpam-2979	33	13	)	)	PUNCT
ejpam-2979	33	14	,	,	PUNCT
ejpam-2979	33	15	506	506	NUM
ejpam-2979	33	16	-	-	SYM
ejpam-2979	33	17	515	515	NUM
ejpam-2979	33	18	508	508	NUM
ejpam-2979	33	19	in	in	ADP
ejpam-2979	33	20	[	[	X
ejpam-2979	33	21	4	4	NUM
ejpam-2979	33	22	]	]	PUNCT
ejpam-2979	33	23	,	,	PUNCT
ejpam-2979	33	24	the	the	DET
ejpam-2979	33	25	authors	author	NOUN
ejpam-2979	33	26	obtain	obtain	VERB
ejpam-2979	33	27	some	some	DET
ejpam-2979	33	28	binomial	binomial	ADJ
ejpam-2979	33	29	summation	summation	NOUN
ejpam-2979	33	30	identities	identity	NOUN
ejpam-2979	33	31	of	of	ADP
ejpam-2979	33	32	sequences	sequence	NOUN
ejpam-2979	33	33	{	{	PUNCT
ejpam-2979	33	34	rn	rn	NOUN
ejpam-2979	33	35	}	}	PUNCT
ejpam-2979	33	36	and	and	CCONJ
ejpam-2979	33	37	{	{	PUNCT
ejpam-2979	33	38	λn	λn	NOUN
ejpam-2979	33	39	}	}	PUNCT
ejpam-2979	33	40	:	:	PUNCT
ejpam-2979	33	41	2n∑	2n∑	X
ejpam-2979	33	42	k=0	k=0	PROPN
ejpam-2979	33	43	(	(	PUNCT
ejpam-2979	33	44	2n	2n	NUM
ejpam-2979	33	45	k	k	NOUN
ejpam-2979	33	46	)	)	PUNCT
ejpam-2979	33	47	(	(	PUNCT
ejpam-2979	33	48	−1)k	−1)k	PROPN
ejpam-2979	33	49	(	(	PUNCT
ejpam-2979	33	50	bc2	bc2	VERB
ejpam-2979	33	51	−	−	PROPN
ejpam-2979	33	52	ac−	ac−	PROPN
ejpam-2979	33	53	1	1	NUM
ejpam-2979	33	54	)	)	PUNCT
ejpam-2979	33	55	2n−k	2n−k	NUM
ejpam-2979	33	56	r2k+1	r2k+1	VERB
ejpam-2979	33	57	=	=	SYM
ejpam-2979	33	58	(	(	PUNCT
ejpam-2979	33	59	ac+	ac+	PROPN
ejpam-2979	33	60	2)2n	2)2n	PROPN
ejpam-2979	33	61	r2n+1	r2n+1	PROPN
ejpam-2979	33	62	,	,	PUNCT
ejpam-2979	33	63	2n∑	2n∑	PROPN
ejpam-2979	33	64	k=0	k=0	PROPN
ejpam-2979	33	65	(	(	PUNCT
ejpam-2979	33	66	2n	2n	NUM
ejpam-2979	33	67	k	k	NOUN
ejpam-2979	33	68	)	)	PUNCT
ejpam-2979	33	69	(	(	PUNCT
ejpam-2979	33	70	−1)k	−1)k	PROPN
ejpam-2979	33	71	(	(	PUNCT
ejpam-2979	33	72	bc2	bc2	VERB
ejpam-2979	33	73	−	−	PROPN
ejpam-2979	33	74	ac−	ac−	PROPN
ejpam-2979	33	75	1	1	NUM
ejpam-2979	33	76	)	)	PUNCT
ejpam-2979	33	77	2n−k	2n−k	NOUN
ejpam-2979	33	78	r2k	r2k	NOUN
ejpam-2979	33	79	=	=	SYM
ejpam-2979	33	80	(	(	PUNCT
ejpam-2979	33	81	ac+	ac+	PROPN
ejpam-2979	33	82	2)2n	2)2n	PROPN
ejpam-2979	33	83	r2n	r2n	NOUN
ejpam-2979	33	84	.	.	PUNCT
ejpam-2979	34	1	2	2	X
ejpam-2979	34	2	.	.	X
ejpam-2979	34	3	some	some	DET
ejpam-2979	34	4	results	result	NOUN
ejpam-2979	34	5	in	in	ADP
ejpam-2979	34	6	this	this	DET
ejpam-2979	34	7	section	section	NOUN
ejpam-2979	34	8	,	,	PUNCT
ejpam-2979	34	9	firstly	firstly	ADV
ejpam-2979	34	10	,	,	PUNCT
ejpam-2979	34	11	we	we	PRON
ejpam-2979	34	12	define	define	VERB
ejpam-2979	34	13	sequences	sequence	NOUN
ejpam-2979	34	14	{	{	PUNCT
ejpam-2979	34	15	gkn	gkn	NOUN
ejpam-2979	34	16	}	}	PUNCT
ejpam-2979	34	17	and	and	CCONJ
ejpam-2979	34	18	{	{	PUNCT
ejpam-2979	34	19	hkn	hkn	NOUN
ejpam-2979	34	20	}	}	PUNCT
ejpam-2979	34	21	and	and	CCONJ
ejpam-2979	34	22	then	then	ADV
ejpam-2979	34	23	derive	derive	VERB
ejpam-2979	34	24	some	some	DET
ejpam-2979	34	25	new	new	ADJ
ejpam-2979	34	26	combinatorial	combinatorial	ADJ
ejpam-2979	34	27	identities	identity	NOUN
ejpam-2979	34	28	for	for	ADP
ejpam-2979	34	29	these	these	DET
ejpam-2979	34	30	sequences	sequence	NOUN
ejpam-2979	34	31	.	.	PUNCT
ejpam-2979	35	1	lemma	lemma	PROPN
ejpam-2979	35	2	1	1	NUM
ejpam-2979	35	3	.	.	PUNCT
ejpam-2979	35	4	for	for	ADP
ejpam-2979	35	5	n	n	PRON
ejpam-2979	35	6	≥	≥	NOUN
ejpam-2979	35	7	0	0	NUM
ejpam-2979	35	8	,	,	PUNCT
ejpam-2979	35	9	the	the	DET
ejpam-2979	35	10	sum	sum	NOUN
ejpam-2979	35	11	n∑	n∑	PROPN
ejpam-2979	35	12	i=0	i=0	PROPN
ejpam-2979	35	13	(	(	PUNCT
ejpam-2979	35	14	n	n	NOUN
ejpam-2979	35	15	i	i	NOUN
ejpam-2979	35	16	)	)	PUNCT
ejpam-2979	35	17	ckiuki	ckiuki	NOUN
ejpam-2979	36	1	=	=	NOUN
ejpam-2979	36	2	gkn	gkn	NOUN
ejpam-2979	36	3	satisfies	satisfy	VERB
ejpam-2979	36	4	the	the	DET
ejpam-2979	36	5	recurrence	recurrence	NOUN
ejpam-2979	36	6	relation	relation	NOUN
ejpam-2979	36	7	gk(n+2	gk(n+2	PROPN
ejpam-2979	36	8	)	)	PUNCT
ejpam-2979	36	9	=	=	SYM
ejpam-2979	36	10	(	(	PUNCT
ejpam-2979	36	11	ckvk	ckvk	VERB
ejpam-2979	36	12	+	+	CCONJ
ejpam-2979	36	13	2	2	NUM
ejpam-2979	36	14	)	)	PUNCT
ejpam-2979	36	15	gk(n+1	gk(n+1	NOUN
ejpam-2979	36	16	)	)	PUNCT
ejpam-2979	36	17	−	−	PROPN
ejpam-2979	37	1	(	(	PUNCT
ejpam-2979	37	2	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	37	3	+	+	CCONJ
ejpam-2979	37	4	ckvk	ckvk	NOUN
ejpam-2979	37	5	+	+	CCONJ
ejpam-2979	37	6	1	1	X
ejpam-2979	37	7	)	)	PUNCT
ejpam-2979	37	8	gkn	gkn	NOUN
ejpam-2979	37	9	,	,	PUNCT
ejpam-2979	37	10	where	where	SCONJ
ejpam-2979	37	11	initial	initial	ADJ
ejpam-2979	37	12	conditions	condition	NOUN
ejpam-2979	37	13	g0	g0	NOUN
ejpam-2979	37	14	=	=	SYM
ejpam-2979	37	15	0	0	NUM
ejpam-2979	37	16	,	,	PUNCT
ejpam-2979	37	17	gk	gk	NOUN
ejpam-2979	37	18	=	=	PUNCT
ejpam-2979	37	19	ckuk	ckuk	NOUN
ejpam-2979	37	20	.	.	PUNCT
ejpam-2979	38	1	proof	proof	NOUN
ejpam-2979	38	2	.	.	PUNCT
ejpam-2979	39	1	considering	consider	VERB
ejpam-2979	39	2	akn	akn	PROPN
ejpam-2979	39	3	=	=	PROPN
ejpam-2979	39	4	cknukn	cknukn	NOUN
ejpam-2979	39	5	and	and	CCONJ
ejpam-2979	39	6	bkn	bkn	PROPN
ejpam-2979	39	7	=	=	PROPN
ejpam-2979	39	8	ck(n+1)uk(n+1	ck(n+1)uk(n+1	PROPN
ejpam-2979	39	9	)	)	PUNCT
ejpam-2979	39	10	in	in	ADP
ejpam-2979	39	11	(	(	PUNCT
ejpam-2979	39	12	1	1	NUM
ejpam-2979	39	13	)	)	PUNCT
ejpam-2979	39	14	,	,	PUNCT
ejpam-2979	39	15	the	the	DET
ejpam-2979	39	16	proof	proof	NOUN
ejpam-2979	39	17	is	be	AUX
ejpam-2979	39	18	completed	complete	VERB
ejpam-2979	39	19	as	as	ADP
ejpam-2979	39	20	similar	similar	ADJ
ejpam-2979	39	21	to	to	ADP
ejpam-2979	39	22	proof	proof	NOUN
ejpam-2979	39	23	technique	technique	NOUN
ejpam-2979	39	24	in	in	ADP
ejpam-2979	39	25	[	[	X
ejpam-2979	39	26	11	11	NUM
ejpam-2979	39	27	]	]	PUNCT
ejpam-2979	39	28	.	.	PUNCT
ejpam-2979	40	1	lemma	lemma	PROPN
ejpam-2979	40	2	2	2	NUM
ejpam-2979	40	3	.	.	PUNCT
ejpam-2979	41	1	the	the	DET
ejpam-2979	41	2	generating	generate	VERB
ejpam-2979	41	3	function	function	NOUN
ejpam-2979	41	4	u(z	u(z	NOUN
ejpam-2979	41	5	)	)	PUNCT
ejpam-2979	41	6	of	of	ADP
ejpam-2979	41	7	n∑	n∑	PROPN
ejpam-2979	41	8	i=0	i=0	PROPN
ejpam-2979	41	9	(	(	PUNCT
ejpam-2979	41	10	n	n	X
ejpam-2979	41	11	i	i	NOUN
ejpam-2979	41	12	)	)	PUNCT
ejpam-2979	41	13	ckiuki	ckiuki	NOUN
ejpam-2979	42	1	=	=	NOUN
ejpam-2979	42	2	gkn	gkn	PROPN
ejpam-2979	42	3	is	be	AUX
ejpam-2979	42	4	given	give	VERB
ejpam-2979	42	5	by	by	ADP
ejpam-2979	42	6	u(z	u(z	NOUN
ejpam-2979	42	7	)	)	PUNCT
ejpam-2979	42	8	=	=	SYM
ejpam-2979	42	9	zkgk	zkgk	NOUN
ejpam-2979	42	10	1−	1−	NUM
ejpam-2979	42	11	(	(	PUNCT
ejpam-2979	42	12	ckvk	ckvk	VERB
ejpam-2979	42	13	+	+	CCONJ
ejpam-2979	42	14	2	2	NUM
ejpam-2979	42	15	)	)	PUNCT
ejpam-2979	42	16	zk	zk	PROPN
ejpam-2979	43	1	+	+	CCONJ
ejpam-2979	43	2	(	(	PUNCT
ejpam-2979	43	3	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	43	4	+	+	CCONJ
ejpam-2979	43	5	ckvk	ckvk	NOUN
ejpam-2979	43	6	+	+	CCONJ
ejpam-2979	43	7	1	1	NUM
ejpam-2979	43	8	)	)	PUNCT
ejpam-2979	43	9	z2k	z2k	NOUN
ejpam-2979	43	10	.	.	PUNCT
ejpam-2979	44	1	proof	proof	NOUN
ejpam-2979	44	2	.	.	PUNCT
ejpam-2979	45	1	observed	observe	VERB
ejpam-2979	45	2	that	that	SCONJ
ejpam-2979	45	3	u(z	u(z	NOUN
ejpam-2979	45	4	)	)	PUNCT
ejpam-2979	45	5	=	=	PUNCT
ejpam-2979	45	6	g0z	g0z	NOUN
ejpam-2979	45	7	0	0	PUNCT
ejpam-2979	46	1	+	+	CCONJ
ejpam-2979	47	1	gkz	gkz	X
ejpam-2979	47	2	k	k	X
ejpam-2979	47	3	+	+	CCONJ
ejpam-2979	47	4	g2kz	g2kz	X
ejpam-2979	47	5	2k	2k	NOUN
ejpam-2979	47	6	+	+	CCONJ
ejpam-2979	47	7	...	...	PUNCT
ejpam-2979	48	1	+	+	NUM
ejpam-2979	48	2	gknz	gknz	PROPN
ejpam-2979	48	3	kn	kn	PROPN
ejpam-2979	48	4	+	+	CCONJ
ejpam-2979	48	5	...	...	PUNCT
ejpam-2979	48	6	zku(z	zku(z	X
ejpam-2979	48	7	)	)	PUNCT
ejpam-2979	48	8	=	=	PUNCT
ejpam-2979	48	9	g0z	g0z	PROPN
ejpam-2979	48	10	k	k	X
ejpam-2979	49	1	+	+	CCONJ
ejpam-2979	49	2	gkz	gkz	VERB
ejpam-2979	49	3	2k	2k	NOUN
ejpam-2979	49	4	+	+	CCONJ
ejpam-2979	49	5	g2kz	g2kz	NOUN
ejpam-2979	49	6	3k	3k	NOUN
ejpam-2979	49	7	+	+	CCONJ
ejpam-2979	49	8	...	...	PUNCT
ejpam-2979	49	9	+	+	CCONJ
ejpam-2979	49	10	gk(n−1)z	gk(n−1)z	PROPN
ejpam-2979	49	11	kn	kn	PROPN
ejpam-2979	49	12	+	+	CCONJ
ejpam-2979	49	13	...	...	PUNCT
ejpam-2979	49	14	z2ku(z	z2ku(z	X
ejpam-2979	49	15	)	)	PUNCT
ejpam-2979	49	16	=	=	PUNCT
ejpam-2979	49	17	g0z	g0z	NOUN
ejpam-2979	49	18	2k	2k	NOUN
ejpam-2979	49	19	+	+	CCONJ
ejpam-2979	49	20	gkz	gkz	X
ejpam-2979	49	21	3k	3k	X
ejpam-2979	49	22	+	+	CCONJ
ejpam-2979	49	23	g2kz	g2kz	X
ejpam-2979	49	24	4k	4k	NOUN
ejpam-2979	49	25	+	+	CCONJ
ejpam-2979	49	26	...	...	PUNCT
ejpam-2979	49	27	+	+	NUM
ejpam-2979	49	28	gk(n−2)z	gk(n−2)z	X
ejpam-2979	49	29	kn	kn	PROPN
ejpam-2979	49	30	+	+	CCONJ
ejpam-2979	49	31	...	...	PUNCT
ejpam-2979	49	32	...	...	PUNCT
ejpam-2979	49	33	from	from	ADP
ejpam-2979	49	34	here	here	ADV
ejpam-2979	49	35	,	,	PUNCT
ejpam-2979	49	36	we	we	PRON
ejpam-2979	49	37	have	have	VERB
ejpam-2979	49	38	u(z	u(z	NOUN
ejpam-2979	49	39	)	)	PUNCT
ejpam-2979	49	40	(	(	PUNCT
ejpam-2979	49	41	1−	1−	NUM
ejpam-2979	49	42	(	(	PUNCT
ejpam-2979	49	43	ckvk	ckvk	VERB
ejpam-2979	49	44	+	+	CCONJ
ejpam-2979	49	45	2	2	X
ejpam-2979	49	46	)	)	PUNCT
ejpam-2979	49	47	zk	zk	PROPN
ejpam-2979	50	1	−	−	PROPN
ejpam-2979	50	2	(	(	PUNCT
ejpam-2979	50	3	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	50	4	+	+	CCONJ
ejpam-2979	50	5	ckvk	ckvk	NOUN
ejpam-2979	50	6	+	+	CCONJ
ejpam-2979	50	7	1	1	NUM
ejpam-2979	50	8	)	)	PUNCT
ejpam-2979	50	9	z2k	z2k	NOUN
ejpam-2979	50	10	)	)	PUNCT
ejpam-2979	51	1	=	=	SYM
ejpam-2979	51	2	zkgk	zkgk	NOUN
ejpam-2979	51	3	+	+	CCONJ
ejpam-2979	51	4	∞∑	∞∑	NUM
ejpam-2979	51	5	i=2	i=2	PROPN
ejpam-2979	51	6	(	(	PUNCT
ejpam-2979	51	7	gki	gki	NOUN
ejpam-2979	51	8	−	−	NOUN
ejpam-2979	51	9	(	(	PUNCT
ejpam-2979	51	10	ckvk	ckvk	VERB
ejpam-2979	51	11	+	+	CCONJ
ejpam-2979	51	12	2	2	X
ejpam-2979	51	13	)	)	PUNCT
ejpam-2979	51	14	gk(i−1	gk(i−1	PROPN
ejpam-2979	51	15	)	)	PUNCT
ejpam-2979	51	16	+	+	CCONJ
ejpam-2979	51	17	(	(	PUNCT
ejpam-2979	51	18	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	51	19	+	+	CCONJ
ejpam-2979	51	20	ckvk	ckvk	NOUN
ejpam-2979	51	21	+	+	CCONJ
ejpam-2979	51	22	1	1	NUM
ejpam-2979	51	23	)	)	PUNCT
ejpam-2979	51	24	gk(i−2	gk(i−2	PROPN
ejpam-2979	51	25	)	)	PUNCT
ejpam-2979	51	26	)	)	PUNCT
ejpam-2979	51	27	zki	zki	NOUN
ejpam-2979	51	28	.	.	PUNCT
ejpam-2979	52	1	from	from	ADP
ejpam-2979	52	2	the	the	DET
ejpam-2979	52	3	recurrence	recurrence	NOUN
ejpam-2979	52	4	relation	relation	NOUN
ejpam-2979	52	5	in	in	ADP
ejpam-2979	52	6	lemma	lemma	PROPN
ejpam-2979	52	7	1	1	NUM
ejpam-2979	52	8	,	,	PUNCT
ejpam-2979	52	9	we	we	PRON
ejpam-2979	52	10	complete	complete	VERB
ejpam-2979	52	11	the	the	DET
ejpam-2979	52	12	proof	proof	NOUN
ejpam-2979	52	13	for	for	ADP
ejpam-2979	52	14	u(z	u(z	NOUN
ejpam-2979	52	15	)	)	PUNCT
ejpam-2979	52	16	.	.	PUNCT
ejpam-2979	53	1	similarly	similarly	ADV
ejpam-2979	53	2	,	,	PUNCT
ejpam-2979	53	3	the	the	DET
ejpam-2979	53	4	proofs	proof	NOUN
ejpam-2979	53	5	of	of	ADP
ejpam-2979	53	6	the	the	DET
ejpam-2979	53	7	following	following	ADJ
ejpam-2979	53	8	lemmas	lemma	NOUN
ejpam-2979	53	9	are	be	AUX
ejpam-2979	53	10	given	give	VERB
ejpam-2979	53	11	as	as	ADP
ejpam-2979	53	12	the	the	DET
ejpam-2979	53	13	proofs	proof	NOUN
ejpam-2979	53	14	of	of	ADP
ejpam-2979	53	15	lemmas	lemmas	PROPN
ejpam-2979	53	16	1	1	NUM
ejpam-2979	53	17	and	and	CCONJ
ejpam-2979	53	18	2	2	NUM
ejpam-2979	53	19	.	.	PUNCT
ejpam-2979	53	20	n.	n.	PROPN
ejpam-2979	53	21	ömür	ömür	PROPN
ejpam-2979	53	22	,	,	PUNCT
ejpam-2979	53	23	c.	c.	PROPN
ejpam-2979	53	24	d.	d.	PROPN
ejpam-2979	53	25	şener	şener	PROPN
ejpam-2979	53	26	/	/	SYM
ejpam-2979	53	27	eur	eur	PROPN
ejpam-2979	53	28	.	.	PUNCT
ejpam-2979	54	1	j.	j.	PROPN
ejpam-2979	54	2	pure	pure	PROPN
ejpam-2979	54	3	appl	appl	PROPN
ejpam-2979	54	4	.	.	PROPN
ejpam-2979	54	5	math	math	PROPN
ejpam-2979	54	6	,	,	PUNCT
ejpam-2979	54	7	10	10	NUM
ejpam-2979	54	8	(	(	PUNCT
ejpam-2979	54	9	3	3	NUM
ejpam-2979	54	10	)	)	PUNCT
ejpam-2979	54	11	(	(	PUNCT
ejpam-2979	54	12	2017	2017	NUM
ejpam-2979	54	13	)	)	PUNCT
ejpam-2979	54	14	,	,	PUNCT
ejpam-2979	54	15	506	506	NUM
ejpam-2979	54	16	-	-	SYM
ejpam-2979	54	17	515	515	NUM
ejpam-2979	54	18	509	509	NUM
ejpam-2979	54	19	lemma	lemma	PROPN
ejpam-2979	54	20	3	3	NUM
ejpam-2979	54	21	.	.	PUNCT
ejpam-2979	54	22	for	for	ADP
ejpam-2979	54	23	n	n	PRON
ejpam-2979	54	24	≥	≥	NOUN
ejpam-2979	54	25	0	0	NUM
ejpam-2979	54	26	,	,	PUNCT
ejpam-2979	54	27	the	the	DET
ejpam-2979	54	28	sum	sum	NOUN
ejpam-2979	54	29	n∑	n∑	PROPN
ejpam-2979	54	30	i=0	i=0	PROPN
ejpam-2979	54	31	(	(	PUNCT
ejpam-2979	54	32	n	n	NOUN
ejpam-2979	54	33	i	i	NOUN
ejpam-2979	54	34	)	)	PUNCT
ejpam-2979	54	35	ckivki	ckivki	NOUN
ejpam-2979	54	36	=	=	PUNCT
ejpam-2979	54	37	hkn	hkn	ADJ
ejpam-2979	54	38	satisfies	satisfie	NOUN
ejpam-2979	54	39	the	the	DET
ejpam-2979	54	40	recurrence	recurrence	NOUN
ejpam-2979	54	41	relation	relation	NOUN
ejpam-2979	54	42	hk(n+2	hk(n+2	NOUN
ejpam-2979	54	43	)	)	PUNCT
ejpam-2979	55	1	=	=	PRON
ejpam-2979	55	2	(	(	PUNCT
ejpam-2979	55	3	ckvk	ckvk	VERB
ejpam-2979	55	4	+	+	CCONJ
ejpam-2979	55	5	2	2	NUM
ejpam-2979	55	6	)	)	PUNCT
ejpam-2979	55	7	hk(n+1	hk(n+1	NUM
ejpam-2979	55	8	)	)	PUNCT
ejpam-2979	56	1	−	−	PROPN
ejpam-2979	56	2	(	(	PUNCT
ejpam-2979	56	3	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	56	4	+	+	CCONJ
ejpam-2979	56	5	ckvk	ckvk	NOUN
ejpam-2979	56	6	+	+	CCONJ
ejpam-2979	56	7	1	1	X
ejpam-2979	56	8	)	)	PUNCT
ejpam-2979	56	9	hkn	hkn	NOUN
ejpam-2979	56	10	,	,	PUNCT
ejpam-2979	56	11	where	where	SCONJ
ejpam-2979	56	12	initial	initial	ADJ
ejpam-2979	56	13	conditions	condition	NOUN
ejpam-2979	56	14	h0	h0	NOUN
ejpam-2979	56	15	=	=	SYM
ejpam-2979	56	16	2	2	NUM
ejpam-2979	56	17	,	,	PUNCT
ejpam-2979	56	18	hk	hk	NOUN
ejpam-2979	56	19	=	=	SYM
ejpam-2979	56	20	2	2	NUM
ejpam-2979	56	21	+	+	NUM
ejpam-2979	56	22	ckvk	ckvk	NOUN
ejpam-2979	56	23	.	.	PUNCT
ejpam-2979	57	1	lemma	lemma	PROPN
ejpam-2979	57	2	4	4	NUM
ejpam-2979	57	3	.	.	PUNCT
ejpam-2979	58	1	the	the	DET
ejpam-2979	58	2	generating	generate	VERB
ejpam-2979	58	3	function	function	NOUN
ejpam-2979	58	4	v	v	ADP
ejpam-2979	58	5	(	(	PUNCT
ejpam-2979	58	6	z	z	NOUN
ejpam-2979	58	7	)	)	PUNCT
ejpam-2979	58	8	of	of	ADP
ejpam-2979	58	9	n∑	n∑	PROPN
ejpam-2979	58	10	i=0	i=0	PROPN
ejpam-2979	58	11	(	(	PUNCT
ejpam-2979	58	12	n	n	NOUN
ejpam-2979	58	13	i	i	NOUN
ejpam-2979	58	14	)	)	PUNCT
ejpam-2979	58	15	ckivki	ckivki	NOUN
ejpam-2979	58	16	=	=	PUNCT
ejpam-2979	58	17	hkn	hkn	NOUN
ejpam-2979	58	18	is	be	AUX
ejpam-2979	58	19	given	give	VERB
ejpam-2979	58	20	by	by	ADP
ejpam-2979	58	21	v	v	PROPN
ejpam-2979	58	22	(	(	PUNCT
ejpam-2979	58	23	z	z	NOUN
ejpam-2979	58	24	)	)	PUNCT
ejpam-2979	58	25	=	=	SYM
ejpam-2979	58	26	zk	zk	PROPN
ejpam-2979	58	27	(	(	PUNCT
ejpam-2979	58	28	hk	hk	PROPN
ejpam-2979	58	29	−	−	PROPN
ejpam-2979	58	30	2	2	NUM
ejpam-2979	58	31	(	(	PUNCT
ejpam-2979	58	32	ckvk	ckvk	VERB
ejpam-2979	58	33	+	+	CCONJ
ejpam-2979	58	34	2	2	NUM
ejpam-2979	58	35	)	)	PUNCT
ejpam-2979	58	36	)	)	PUNCT
ejpam-2979	59	1	+	+	CCONJ
ejpam-2979	59	2	2	2	NUM
ejpam-2979	59	3	1−	1−	NUM
ejpam-2979	59	4	(	(	PUNCT
ejpam-2979	59	5	ckvk	ckvk	VERB
ejpam-2979	59	6	+	+	CCONJ
ejpam-2979	59	7	2	2	NUM
ejpam-2979	59	8	)	)	PUNCT
ejpam-2979	59	9	zk	zk	PROPN
ejpam-2979	60	1	+	+	CCONJ
ejpam-2979	60	2	(	(	PUNCT
ejpam-2979	60	3	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	60	4	+	+	CCONJ
ejpam-2979	60	5	ckvk	ckvk	NOUN
ejpam-2979	60	6	+	+	CCONJ
ejpam-2979	60	7	1	1	NUM
ejpam-2979	60	8	)	)	PUNCT
ejpam-2979	60	9	z2k	z2k	NOUN
ejpam-2979	60	10	.	.	PUNCT
ejpam-2979	61	1	if	if	SCONJ
ejpam-2979	61	2	ckαk	ckαk	VERB
ejpam-2979	61	3	+	+	CCONJ
ejpam-2979	61	4	1	1	NUM
ejpam-2979	61	5	and	and	CCONJ
ejpam-2979	61	6	ckβk	ckβk	NOUN
ejpam-2979	61	7	+	+	CCONJ
ejpam-2979	61	8	1	1	NUM
ejpam-2979	61	9	are	be	AUX
ejpam-2979	61	10	the	the	DET
ejpam-2979	61	11	roots	root	NOUN
ejpam-2979	61	12	of	of	ADP
ejpam-2979	61	13	equation	equation	NOUN
ejpam-2979	62	1	x2	x2	PROPN
ejpam-2979	62	2	−	−	PROPN
ejpam-2979	62	3	(	(	PUNCT
ejpam-2979	62	4	ckvk	ckvk	VERB
ejpam-2979	62	5	+	+	CCONJ
ejpam-2979	62	6	2	2	NUM
ejpam-2979	62	7	)	)	PUNCT
ejpam-2979	62	8	x+	x+	PUNCT
ejpam-2979	62	9	(	(	PUNCT
ejpam-2979	62	10	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	62	11	+	+	CCONJ
ejpam-2979	62	12	ckvk	ckvk	NOUN
ejpam-2979	62	13	+	+	CCONJ
ejpam-2979	62	14	1	1	NUM
ejpam-2979	62	15	)	)	PUNCT
ejpam-2979	62	16	=	=	SYM
ejpam-2979	62	17	0	0	NUM
ejpam-2979	62	18	,	,	PUNCT
ejpam-2979	62	19	binet	binet	NOUN
ejpam-2979	62	20	formulae	formulae	NOUN
ejpam-2979	62	21	of	of	ADP
ejpam-2979	62	22	sequences	sequence	NOUN
ejpam-2979	62	23	{	{	PUNCT
ejpam-2979	62	24	gkn	gkn	NOUN
ejpam-2979	62	25	}	}	PUNCT
ejpam-2979	62	26	and	and	CCONJ
ejpam-2979	62	27	{	{	PUNCT
ejpam-2979	62	28	hkn	hkn	NOUN
ejpam-2979	62	29	}	}	PUNCT
ejpam-2979	62	30	are	be	AUX
ejpam-2979	62	31	gkn	gkn	ADJ
ejpam-2979	62	32	=	=	SYM
ejpam-2979	62	33	(	(	PUNCT
ejpam-2979	62	34	ckαk	ckαk	X
ejpam-2979	62	35	+	+	CCONJ
ejpam-2979	62	36	1	1	NUM
ejpam-2979	62	37	)	)	PUNCT
ejpam-2979	62	38	n	n	NOUN
ejpam-2979	62	39	−	−	PROPN
ejpam-2979	62	40	(	(	PUNCT
ejpam-2979	62	41	ckβk	ckβk	VERB
ejpam-2979	62	42	+	+	CCONJ
ejpam-2979	62	43	1	1	NUM
ejpam-2979	62	44	)	)	PUNCT
ejpam-2979	62	45	n	n	NOUN
ejpam-2979	62	46	α−	α−	ADP
ejpam-2979	62	47	β	β	X
ejpam-2979	62	48	and	and	CCONJ
ejpam-2979	62	49	hkn	hkn	NOUN
ejpam-2979	62	50	=	=	SYM
ejpam-2979	62	51	(	(	PUNCT
ejpam-2979	62	52	ckαk	ckαk	X
ejpam-2979	62	53	+	+	CCONJ
ejpam-2979	62	54	1	1	NUM
ejpam-2979	62	55	)	)	PUNCT
ejpam-2979	62	56	n	n	NOUN
ejpam-2979	62	57	+	+	CCONJ
ejpam-2979	62	58	(	(	PUNCT
ejpam-2979	62	59	ckβk	ckβk	VERB
ejpam-2979	62	60	+	+	CCONJ
ejpam-2979	62	61	1	1	NUM
ejpam-2979	62	62	)	)	PUNCT
ejpam-2979	62	63	n	n	CCONJ
ejpam-2979	62	64	,	,	PUNCT
ejpam-2979	62	65	respectively	respectively	ADV
ejpam-2979	62	66	.	.	PUNCT
ejpam-2979	63	1	it	it	PRON
ejpam-2979	63	2	is	be	AUX
ejpam-2979	63	3	clear	clear	ADJ
ejpam-2979	63	4	that	that	SCONJ
ejpam-2979	63	5	g−kn	g−kn	PROPN
ejpam-2979	63	6	=	=	PRON
ejpam-2979	64	1	−	−	PROPN
ejpam-2979	64	2	(	(	PUNCT
ejpam-2979	64	3	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	64	4	+	+	CCONJ
ejpam-2979	64	5	ckvk	ckvk	NOUN
ejpam-2979	64	6	+	+	CCONJ
ejpam-2979	64	7	1	1	NUM
ejpam-2979	64	8	)	)	PUNCT
ejpam-2979	64	9	−n	−n	ADJ
ejpam-2979	64	10	gkn	gkn	NOUN
ejpam-2979	64	11	,	,	PUNCT
ejpam-2979	64	12	g2kn	g2kn	PUNCT
ejpam-2979	64	13	=	=	SYM
ejpam-2979	64	14	gknhkn	gknhkn	NOUN
ejpam-2979	64	15	(	(	PUNCT
ejpam-2979	64	16	2	2	NUM
ejpam-2979	64	17	)	)	PUNCT
ejpam-2979	64	18	and	and	CCONJ
ejpam-2979	64	19	h−kn	h−kn	NUM
ejpam-2979	65	1	=	=	SYM
ejpam-2979	65	2	(	(	PUNCT
ejpam-2979	65	3	(	(	PUNCT
ejpam-2979	65	4	−q)kc2k	−q)kc2k	VERB
ejpam-2979	65	5	+	+	CCONJ
ejpam-2979	65	6	ckvk	ckvk	NOUN
ejpam-2979	65	7	+	+	CCONJ
ejpam-2979	65	8	1	1	NUM
ejpam-2979	65	9	)	)	PUNCT
ejpam-2979	65	10	−n	−n	ADJ
ejpam-2979	65	11	hkn	hkn	NOUN
ejpam-2979	65	12	.	.	PUNCT
ejpam-2979	66	1	now	now	ADV
ejpam-2979	66	2	,	,	PUNCT
ejpam-2979	66	3	we	we	PRON
ejpam-2979	66	4	define	define	VERB
ejpam-2979	66	5	a	a	DET
ejpam-2979	66	6	2×	2×	NUM
ejpam-2979	66	7	2	2	NUM
ejpam-2979	66	8	matrix	matrix	NOUN
ejpam-2979	66	9	a	a	PRON
ejpam-2979	67	1	and	and	CCONJ
ejpam-2979	67	2	then	then	ADV
ejpam-2979	67	3	we	we	PRON
ejpam-2979	67	4	give	give	VERB
ejpam-2979	67	5	some	some	DET
ejpam-2979	67	6	new	new	ADJ
ejpam-2979	67	7	results	result	NOUN
ejpam-2979	67	8	for	for	ADP
ejpam-2979	67	9	the	the	DET
ejpam-2979	67	10	sequences	sequence	NOUN
ejpam-2979	67	11	{	{	PUNCT
ejpam-2979	67	12	gkn	gkn	NOUN
ejpam-2979	67	13	}	}	PUNCT
ejpam-2979	67	14	and	and	CCONJ
ejpam-2979	67	15	{	{	PUNCT
ejpam-2979	67	16	hkn	hkn	NOUN
ejpam-2979	67	17	}	}	PUNCT
ejpam-2979	67	18	by	by	ADP
ejpam-2979	67	19	matrix	matrix	NOUN
ejpam-2979	67	20	methods	method	NOUN
ejpam-2979	67	21	.	.	PUNCT
ejpam-2979	68	1	consider	consider	VERB
ejpam-2979	68	2	the	the	DET
ejpam-2979	68	3	2×	2×	NUM
ejpam-2979	68	4	2	2	NUM
ejpam-2979	68	5	matrix	matrix	NOUN
ejpam-2979	68	6	a	a	PRON
ejpam-2979	68	7	as	as	SCONJ
ejpam-2979	68	8	follows	follow	VERB
ejpam-2979	68	9	:	:	PUNCT
ejpam-2979	68	10	a	a	DET
ejpam-2979	68	11	=	=	X
ejpam-2979	68	12	[	[	PUNCT
ejpam-2979	68	13	ckvk	ckvk	NOUN
ejpam-2979	69	1	+	+	CCONJ
ejpam-2979	69	2	2	2	NUM
ejpam-2979	69	3	−	−	NOUN
ejpam-2979	69	4	(	(	PUNCT
ejpam-2979	69	5	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	69	6	+	+	CCONJ
ejpam-2979	69	7	ckvk	ckvk	NOUN
ejpam-2979	69	8	+	+	CCONJ
ejpam-2979	69	9	1	1	NUM
ejpam-2979	69	10	)	)	PUNCT
ejpam-2979	69	11	1	1	NUM
ejpam-2979	69	12	0	0	NUM
ejpam-2979	69	13	]	]	PUNCT
ejpam-2979	69	14	.	.	PUNCT
ejpam-2979	70	1	the	the	DET
ejpam-2979	70	2	eigenvalues	eigenvalue	NOUN
ejpam-2979	70	3	of	of	ADP
ejpam-2979	70	4	the	the	DET
ejpam-2979	70	5	matrix	matrix	NOUN
ejpam-2979	70	6	a	a	PRON
ejpam-2979	70	7	are	be	AUX
ejpam-2979	70	8	λ1	λ1	ADJ
ejpam-2979	70	9	=	=	SYM
ejpam-2979	70	10	ckαk	ckαk	NOUN
ejpam-2979	71	1	+	+	CCONJ
ejpam-2979	71	2	1	1	NUM
ejpam-2979	71	3	,	,	PUNCT
ejpam-2979	71	4	λ2	λ2	NOUN
ejpam-2979	71	5	=	=	SYM
ejpam-2979	71	6	ckβk	ckβk	PROPN
ejpam-2979	71	7	+	+	X
ejpam-2979	71	8	1	1	X
ejpam-2979	71	9	.	.	X
ejpam-2979	71	10	also	also	ADV
ejpam-2979	71	11	λ1	λ1	ADJ
ejpam-2979	71	12	,	,	PUNCT
ejpam-2979	71	13	λ2	λ2	NOUN
ejpam-2979	71	14	are	be	AUX
ejpam-2979	71	15	distinct	distinct	ADJ
ejpam-2979	71	16	.	.	PUNCT
ejpam-2979	72	1	let	let	VERB
ejpam-2979	72	2	v	v	PART
ejpam-2979	72	3	be	be	AUX
ejpam-2979	72	4	the	the	DET
ejpam-2979	72	5	2×	2×	NUM
ejpam-2979	72	6	2	2	NUM
ejpam-2979	72	7	matrix	matrix	NOUN
ejpam-2979	72	8	defined	define	VERB
ejpam-2979	72	9	as	as	SCONJ
ejpam-2979	72	10	follows	follow	VERB
ejpam-2979	72	11	:	:	PUNCT
ejpam-2979	72	12	v	v	X
ejpam-2979	72	13	=	=	PUNCT
ejpam-2979	72	14	[	[	PUNCT
ejpam-2979	72	15	ckαk	ckαk	X
ejpam-2979	72	16	+	+	CCONJ
ejpam-2979	72	17	1	1	NUM
ejpam-2979	72	18	ckβk	ckβk	NOUN
ejpam-2979	72	19	+	+	CCONJ
ejpam-2979	72	20	1	1	NUM
ejpam-2979	72	21	1	1	NUM
ejpam-2979	72	22	1	1	NUM
ejpam-2979	72	23	]	]	PUNCT
ejpam-2979	72	24	.	.	PUNCT
ejpam-2979	73	1	one	one	PRON
ejpam-2979	73	2	can	can	AUX
ejpam-2979	73	3	easily	easily	ADV
ejpam-2979	73	4	verify	verify	VERB
ejpam-2979	73	5	that	that	SCONJ
ejpam-2979	73	6	av	av	PRON
ejpam-2979	73	7	=	=	PUNCT
ejpam-2979	73	8	v	v	ADP
ejpam-2979	73	9	d1	d1	NOUN
ejpam-2979	73	10	,	,	PUNCT
ejpam-2979	73	11	n.	n.	NOUN
ejpam-2979	73	12	ömür	ömür	NOUN
ejpam-2979	73	13	,	,	PUNCT
ejpam-2979	73	14	c.	c.	PROPN
ejpam-2979	73	15	d.	d.	PROPN
ejpam-2979	73	16	şener	şener	PROPN
ejpam-2979	73	17	/	/	SYM
ejpam-2979	73	18	eur	eur	PROPN
ejpam-2979	73	19	.	.	PUNCT
ejpam-2979	74	1	j.	j.	PROPN
ejpam-2979	74	2	pure	pure	PROPN
ejpam-2979	74	3	appl	appl	PROPN
ejpam-2979	74	4	.	.	PROPN
ejpam-2979	74	5	math	math	PROPN
ejpam-2979	74	6	,	,	PUNCT
ejpam-2979	74	7	10	10	NUM
ejpam-2979	74	8	(	(	PUNCT
ejpam-2979	74	9	3	3	NUM
ejpam-2979	74	10	)	)	PUNCT
ejpam-2979	74	11	(	(	PUNCT
ejpam-2979	74	12	2017	2017	NUM
ejpam-2979	74	13	)	)	PUNCT
ejpam-2979	74	14	,	,	PUNCT
ejpam-2979	74	15	506	506	NUM
ejpam-2979	74	16	-	-	SYM
ejpam-2979	74	17	515	515	NUM
ejpam-2979	74	18	510	510	NUM
ejpam-2979	74	19	where	where	SCONJ
ejpam-2979	74	20	d1	d1	NOUN
ejpam-2979	74	21	=	=	SYM
ejpam-2979	74	22	diag	diag	PROPN
ejpam-2979	74	23	(	(	PUNCT
ejpam-2979	74	24	λ1	λ1	ADJ
ejpam-2979	74	25	,	,	PUNCT
ejpam-2979	74	26	λ2	λ2	PROPN
ejpam-2979	74	27	)	)	PUNCT
ejpam-2979	74	28	.	.	PUNCT
ejpam-2979	75	1	since	since	SCONJ
ejpam-2979	75	2	detv	detv	ADJ
ejpam-2979	75	3	6=	6=	NUM
ejpam-2979	75	4	0	0	NUM
ejpam-2979	75	5	,	,	PUNCT
ejpam-2979	75	6	the	the	DET
ejpam-2979	75	7	matrix	matrix	NOUN
ejpam-2979	75	8	v	v	ADP
ejpam-2979	75	9	invertible	invertible	ADJ
ejpam-2979	75	10	.	.	PUNCT
ejpam-2979	76	1	so	so	ADV
ejpam-2979	76	2	,	,	PUNCT
ejpam-2979	76	3	we	we	PRON
ejpam-2979	76	4	write	write	VERB
ejpam-2979	76	5	d1	d1	PROPN
ejpam-2979	76	6	=	=	SYM
ejpam-2979	76	7	v	v	ADP
ejpam-2979	76	8	−1av	−1av	PROPN
ejpam-2979	76	9	.	.	PUNCT
ejpam-2979	77	1	thus	thus	ADV
ejpam-2979	77	2	,	,	PUNCT
ejpam-2979	77	3	the	the	DET
ejpam-2979	77	4	matrix	matrix	NOUN
ejpam-2979	77	5	a	a	PRON
ejpam-2979	77	6	is	be	AUX
ejpam-2979	77	7	similar	similar	ADJ
ejpam-2979	77	8	to	to	ADP
ejpam-2979	77	9	the	the	DET
ejpam-2979	77	10	diagonal	diagonal	ADJ
ejpam-2979	77	11	matrix	matrix	NOUN
ejpam-2979	77	12	d1	d1	NOUN
ejpam-2979	77	13	.	.	PUNCT
ejpam-2979	78	1	we	we	PRON
ejpam-2979	78	2	obtain	obtain	VERB
ejpam-2979	78	3	an	an	DET
ejpam-2979	78	4	=	=	SYM
ejpam-2979	78	5	v	v	NUM
ejpam-2979	78	6	dn	dn	PROPN
ejpam-2979	78	7	1v	1v	NUM
ejpam-2979	78	8	−1	−1	NOUN
ejpam-2979	78	9	=	=	SYM
ejpam-2979	78	10	1	1	NUM
ejpam-2979	78	11	ckuk	ckuk	NOUN
ejpam-2979	78	12			NOUN
ejpam-2979	78	13	gk(n+1	gk(n+1	NOUN
ejpam-2979	78	14	)	)	PUNCT
ejpam-2979	78	15	−	−	PROPN
ejpam-2979	79	1	(	(	PUNCT
ejpam-2979	79	2	c2k	c2k	X
ejpam-2979	79	3	(	(	PUNCT
ejpam-2979	79	4	−q)k	−q)k	NOUN
ejpam-2979	79	5	+	+	CCONJ
ejpam-2979	79	6	ckvk	ckvk	VERB
ejpam-2979	79	7	+	+	CCONJ
ejpam-2979	79	8	1	1	X
ejpam-2979	79	9	)	)	PUNCT
ejpam-2979	79	10	gkn	gkn	NOUN
ejpam-2979	79	11	gkn	gkn	NOUN
ejpam-2979	79	12	−	−	PROPN
ejpam-2979	79	13	(	(	PUNCT
ejpam-2979	79	14	c2k	c2k	X
ejpam-2979	79	15	(	(	PUNCT
ejpam-2979	79	16	−q)k	−q)k	NOUN
ejpam-2979	79	17	+	+	CCONJ
ejpam-2979	79	18	ckvk	ckvk	VERB
ejpam-2979	79	19	+	+	CCONJ
ejpam-2979	79	20	1	1	X
ejpam-2979	79	21	)	)	PUNCT
ejpam-2979	79	22	gk(n−1	gk(n−1	PROPN
ejpam-2979	79	23	)	)	PUNCT
ejpam-2979	79	24			NOUN
ejpam-2979	79	25	.	.	PUNCT
ejpam-2979	80	1	clearly	clearly	ADV
ejpam-2979	80	2	,	,	PUNCT
ejpam-2979	80	3	the	the	DET
ejpam-2979	80	4	matrix	matrix	NOUN
ejpam-2979	80	5	an	an	DET
ejpam-2979	80	6	satisfies	satisfie	NOUN
ejpam-2979	80	7	the	the	DET
ejpam-2979	80	8	recurrence	recurrence	NOUN
ejpam-2979	80	9	relation	relation	NOUN
ejpam-2979	80	10	:	:	PUNCT
ejpam-2979	80	11	for	for	ADP
ejpam-2979	80	12	n	n	PROPN
ejpam-2979	80	13	>	>	X
ejpam-2979	80	14	0	0	NUM
ejpam-2979	80	15	,	,	PUNCT
ejpam-2979	80	16	an+1	an+1	NOUN
ejpam-2979	80	17	=	=	SYM
ejpam-2979	80	18	(	(	PUNCT
ejpam-2979	80	19	ckvk	ckvk	VERB
ejpam-2979	80	20	+	+	CCONJ
ejpam-2979	80	21	2	2	NUM
ejpam-2979	80	22	)	)	PUNCT
ejpam-2979	80	23	an	an	DET
ejpam-2979	80	24	−	−	PROPN
ejpam-2979	80	25	(	(	PUNCT
ejpam-2979	80	26	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	80	27	+	+	CCONJ
ejpam-2979	80	28	ckvk	ckvk	NOUN
ejpam-2979	80	29	+	+	CCONJ
ejpam-2979	80	30	1	1	NUM
ejpam-2979	80	31	)	)	PUNCT
ejpam-2979	80	32	an−1	an−1	ADJ
ejpam-2979	80	33	,	,	PUNCT
ejpam-2979	80	34	where	where	SCONJ
ejpam-2979	80	35	initial	initial	ADJ
ejpam-2979	80	36	conditions	condition	NOUN
ejpam-2979	80	37	a0	a0	NOUN
ejpam-2979	80	38	=	=	SYM
ejpam-2979	80	39	0	0	PROPN
ejpam-2979	80	40	,	,	PUNCT
ejpam-2979	80	41	a1	a1	NOUN
ejpam-2979	80	42	=	=	NOUN
ejpam-2979	80	43	a.	a.	NOUN
ejpam-2979	80	44	also	also	ADV
ejpam-2979	80	45	by	by	ADP
ejpam-2979	80	46	matrix	matrix	NOUN
ejpam-2979	80	47	methods	method	NOUN
ejpam-2979	80	48	,	,	PUNCT
ejpam-2979	80	49	it	it	PRON
ejpam-2979	80	50	is	be	AUX
ejpam-2979	80	51	clearly	clearly	ADV
ejpam-2979	80	52	that	that	SCONJ
ejpam-2979	80	53	an	an	DET
ejpam-2979	80	54	[	[	PUNCT
ejpam-2979	80	55	gk	gk	PROPN
ejpam-2979	80	56	g0	g0	NOUN
ejpam-2979	80	57	]	]	PUNCT
ejpam-2979	81	1	=	=	PUNCT
ejpam-2979	81	2	[	[	PUNCT
ejpam-2979	81	3	gk(n+1	gk(n+1	NOUN
ejpam-2979	81	4	)	)	PUNCT
ejpam-2979	81	5	gkn	gkn	NOUN
ejpam-2979	81	6	]	]	PUNCT
ejpam-2979	81	7	.	.	PUNCT
ejpam-2979	82	1	(	(	PUNCT
ejpam-2979	82	2	3	3	X
ejpam-2979	82	3	)	)	PUNCT
ejpam-2979	82	4	for	for	ADP
ejpam-2979	82	5	n	n	PRON
ejpam-2979	82	6	≥	≥	NOUN
ejpam-2979	82	7	0	0	NUM
ejpam-2979	82	8	,	,	PUNCT
ejpam-2979	82	9	if	if	SCONJ
ejpam-2979	82	10	we	we	PRON
ejpam-2979	82	11	consider	consider	VERB
ejpam-2979	82	12	the	the	DET
ejpam-2979	82	13	fact	fact	NOUN
ejpam-2979	82	14	that	that	SCONJ
ejpam-2979	82	15	det(an	det(an	NOUN
ejpam-2979	82	16	)	)	PUNCT
ejpam-2979	82	17	=	=	SYM
ejpam-2979	82	18	(	(	PUNCT
ejpam-2979	82	19	deta)n	deta)n	PROPN
ejpam-2979	82	20	,	,	PUNCT
ejpam-2979	82	21	then	then	ADV
ejpam-2979	82	22	we	we	PRON
ejpam-2979	82	23	obtain	obtain	VERB
ejpam-2979	82	24	the	the	DET
ejpam-2979	82	25	cassini	cassini	ADJ
ejpam-2979	82	26	identity	identity	NOUN
ejpam-2979	82	27	g2kn	g2kn	ADV
ejpam-2979	82	28	−	−	ADP
ejpam-2979	82	29	gk(n+1)gk(n−1	gk(n+1)gk(n−1	ADJ
ejpam-2979	82	30	)	)	PUNCT
ejpam-2979	82	31	=	=	SYM
ejpam-2979	83	1	(	(	PUNCT
ejpam-2979	83	2	c2k	c2k	X
ejpam-2979	83	3	(	(	PUNCT
ejpam-2979	83	4	−q)k	−q)k	NOUN
ejpam-2979	83	5	+	+	CCONJ
ejpam-2979	83	6	ckvk	ckvk	VERB
ejpam-2979	83	7	+	+	CCONJ
ejpam-2979	83	8	1	1	NUM
ejpam-2979	83	9	)	)	PUNCT
ejpam-2979	83	10	n−1	n−1	PROPN
ejpam-2979	83	11	g2k	g2k	NOUN
ejpam-2979	83	12	.	.	PUNCT
ejpam-2979	84	1	for	for	ADP
ejpam-2979	84	2	example	example	NOUN
ejpam-2979	84	3	,	,	PUNCT
ejpam-2979	84	4	for	for	ADP
ejpam-2979	84	5	k	k	PROPN
ejpam-2979	84	6	=	=	PUNCT
ejpam-2979	84	7	c	c	X
ejpam-2979	85	1	=	=	PUNCT
ejpam-2979	85	2	p	p	NOUN
ejpam-2979	85	3	=	=	X
ejpam-2979	85	4	q	q	NOUN
ejpam-2979	85	5	=	=	NOUN
ejpam-2979	85	6	1	1	NUM
ejpam-2979	85	7	,	,	PUNCT
ejpam-2979	85	8	we	we	PRON
ejpam-2979	85	9	write	write	VERB
ejpam-2979	85	10	f	f	PROPN
ejpam-2979	85	11	2	2	NUM
ejpam-2979	85	12	2n−f2n+1f2n−1	2n−f2n+1f2n−1	NUM
ejpam-2979	85	13	=	=	SYM
ejpam-2979	85	14	−1	−1	NOUN
ejpam-2979	85	15	(	(	PUNCT
ejpam-2979	85	16	see	see	VERB
ejpam-2979	85	17	page	page	NOUN
ejpam-2979	85	18	74	74	NUM
ejpam-2979	85	19	,	,	PUNCT
ejpam-2979	85	20	[	[	X
ejpam-2979	85	21	12	12	NUM
ejpam-2979	85	22	]	]	PUNCT
ejpam-2979	85	23	)	)	PUNCT
ejpam-2979	85	24	.	.	PUNCT
ejpam-2979	86	1	similarly	similarly	ADV
ejpam-2979	86	2	a−n	a−n	PROPN
ejpam-2979	86	3	=	=	SYM
ejpam-2979	86	4	1	1	NUM
ejpam-2979	86	5	ckuk	ckuk	NOUN
ejpam-2979	86	6	(	(	PUNCT
ejpam-2979	86	7	c2k	c2k	X
ejpam-2979	86	8	(	(	PUNCT
ejpam-2979	86	9	−q)k	−q)k	NOUN
ejpam-2979	86	10	+	+	CCONJ
ejpam-2979	86	11	ckvk	ckvk	VERB
ejpam-2979	86	12	+	+	CCONJ
ejpam-2979	86	13	1	1	NUM
ejpam-2979	86	14	)	)	PUNCT
ejpam-2979	86	15	n	n	NOUN
ejpam-2979	86	16	×	×	NOUN
ejpam-2979	86	17	[	[	PUNCT
ejpam-2979	86	18	−	−	PROPN
ejpam-2979	86	19	(	(	PUNCT
ejpam-2979	86	20	c2k	c2k	X
ejpam-2979	86	21	(	(	PUNCT
ejpam-2979	86	22	−q)k	−q)k	NOUN
ejpam-2979	86	23	+	+	CCONJ
ejpam-2979	86	24	ckvk	ckvk	VERB
ejpam-2979	86	25	+	+	CCONJ
ejpam-2979	86	26	1	1	X
ejpam-2979	86	27	)	)	PUNCT
ejpam-2979	86	28	gk(n−1	gk(n−1	PROPN
ejpam-2979	86	29	)	)	PUNCT
ejpam-2979	86	30	(	(	PUNCT
ejpam-2979	86	31	c2k	c2k	X
ejpam-2979	86	32	(	(	PUNCT
ejpam-2979	86	33	−q)k	−q)k	NOUN
ejpam-2979	86	34	+	+	CCONJ
ejpam-2979	86	35	ckvk	ckvk	VERB
ejpam-2979	86	36	+	+	CCONJ
ejpam-2979	86	37	1	1	X
ejpam-2979	86	38	)	)	PUNCT
ejpam-2979	86	39	gkn	gkn	NOUN
ejpam-2979	86	40	−gkn	−gkn	NOUN
ejpam-2979	86	41	gk(n+1	gk(n+1	NOUN
ejpam-2979	86	42	)	)	PUNCT
ejpam-2979	86	43	]	]	PUNCT
ejpam-2979	86	44	and	and	CCONJ
ejpam-2979	86	45	a−n	a−n	PROPN
ejpam-2979	86	46	[	[	PUNCT
ejpam-2979	86	47	gk	gk	PROPN
ejpam-2979	86	48	g0	g0	PROPN
ejpam-2979	86	49	]	]	PUNCT
ejpam-2979	87	1	=	=	PUNCT
ejpam-2979	87	2	[	[	PUNCT
ejpam-2979	87	3	gk(−n+1	gk(−n+1	NOUN
ejpam-2979	87	4	)	)	PUNCT
ejpam-2979	87	5	g−kn	g−kn	NOUN
ejpam-2979	87	6	]	]	PUNCT
ejpam-2979	87	7	.	.	PUNCT
ejpam-2979	88	1	(	(	PUNCT
ejpam-2979	88	2	4	4	NUM
ejpam-2979	88	3	)	)	PUNCT
ejpam-2979	88	4	by	by	ADP
ejpam-2979	88	5	considering	consider	VERB
ejpam-2979	88	6	sequence	sequence	NOUN
ejpam-2979	88	7	{	{	PUNCT
ejpam-2979	88	8	hkn	hkn	NOUN
ejpam-2979	88	9	}	}	PUNCT
ejpam-2979	88	10	,	,	PUNCT
ejpam-2979	88	11	we	we	PRON
ejpam-2979	88	12	write	write	VERB
ejpam-2979	88	13	the	the	DET
ejpam-2979	88	14	simple	simple	ADJ
ejpam-2979	88	15	relation	relation	NOUN
ejpam-2979	88	16	between	between	ADP
ejpam-2979	88	17	the	the	DET
ejpam-2979	88	18	vector	vector	NOUN
ejpam-2979	88	19	of	of	ADP
ejpam-2979	88	20	sequence	sequence	NOUN
ejpam-2979	88	21	{	{	PUNCT
ejpam-2979	88	22	hkn	hkn	NOUN
ejpam-2979	88	23	}	}	PUNCT
ejpam-2979	88	24	and	and	CCONJ
ejpam-2979	88	25	generating	generate	VERB
ejpam-2979	88	26	matrix	matrix	NOUN
ejpam-2979	88	27	of	of	ADP
ejpam-2979	88	28	sequence	sequence	NOUN
ejpam-2979	88	29	{	{	PUNCT
ejpam-2979	88	30	gkn	gkn	NOUN
ejpam-2979	88	31	}	}	PUNCT
ejpam-2979	88	32	:	:	PUNCT
ejpam-2979	88	33	[	[	PUNCT
ejpam-2979	88	34	hk(n+1	hk(n+1	X
ejpam-2979	88	35	)	)	PUNCT
ejpam-2979	88	36	hkn	hkn	NOUN
ejpam-2979	88	37	]	]	PUNCT
ejpam-2979	88	38	=	=	SYM
ejpam-2979	88	39	1	1	NUM
ejpam-2979	88	40	ckuk	ckuk	NOUN
ejpam-2979	88	41			NOUN
ejpam-2979	88	42	gk(n+1	gk(n+1	NOUN
ejpam-2979	88	43	)	)	PUNCT
ejpam-2979	88	44	−	−	PROPN
ejpam-2979	89	1	(	(	PUNCT
ejpam-2979	89	2	c2k	c2k	X
ejpam-2979	89	3	(	(	PUNCT
ejpam-2979	89	4	−q)k	−q)k	NOUN
ejpam-2979	89	5	+	+	CCONJ
ejpam-2979	89	6	ckvk	ckvk	VERB
ejpam-2979	89	7	+	+	CCONJ
ejpam-2979	89	8	1	1	X
ejpam-2979	89	9	)	)	PUNCT
ejpam-2979	89	10	gkn	gkn	NOUN
ejpam-2979	89	11	gkn	gkn	NOUN
ejpam-2979	89	12	−	−	PROPN
ejpam-2979	89	13	(	(	PUNCT
ejpam-2979	89	14	c2k	c2k	X
ejpam-2979	89	15	(	(	PUNCT
ejpam-2979	89	16	−q)k	−q)k	NOUN
ejpam-2979	89	17	+	+	CCONJ
ejpam-2979	89	18	ckvk	ckvk	VERB
ejpam-2979	89	19	+	+	CCONJ
ejpam-2979	89	20	1	1	X
ejpam-2979	89	21	)	)	PUNCT
ejpam-2979	89	22	gk(n−1	gk(n−1	PROPN
ejpam-2979	89	23	)	)	PUNCT
ejpam-2979	89	24			NOUN
ejpam-2979	89	25	[	[	PUNCT
ejpam-2979	89	26	ckvk	ckvk	NOUN
ejpam-2979	89	27	+	+	CCONJ
ejpam-2979	89	28	2	2	NUM
ejpam-2979	89	29	2	2	NUM
ejpam-2979	89	30	]	]	PUNCT
ejpam-2979	89	31	.	.	PUNCT
ejpam-2979	90	1	n.	n.	PROPN
ejpam-2979	90	2	ömür	ömür	PROPN
ejpam-2979	90	3	,	,	PUNCT
ejpam-2979	90	4	c.	c.	PROPN
ejpam-2979	90	5	d.	d.	PROPN
ejpam-2979	90	6	şener	şener	PROPN
ejpam-2979	90	7	/	/	SYM
ejpam-2979	90	8	eur	eur	PROPN
ejpam-2979	90	9	.	.	PUNCT
ejpam-2979	91	1	j.	j.	PROPN
ejpam-2979	91	2	pure	pure	PROPN
ejpam-2979	91	3	appl	appl	PROPN
ejpam-2979	91	4	.	.	PROPN
ejpam-2979	91	5	math	math	PROPN
ejpam-2979	91	6	,	,	PUNCT
ejpam-2979	91	7	10	10	NUM
ejpam-2979	91	8	(	(	PUNCT
ejpam-2979	91	9	3	3	NUM
ejpam-2979	91	10	)	)	PUNCT
ejpam-2979	91	11	(	(	PUNCT
ejpam-2979	91	12	2017	2017	NUM
ejpam-2979	91	13	)	)	PUNCT
ejpam-2979	91	14	,	,	PUNCT
ejpam-2979	91	15	506	506	NUM
ejpam-2979	91	16	-	-	SYM
ejpam-2979	91	17	515	515	NUM
ejpam-2979	91	18	511	511	NUM
ejpam-2979	91	19	theorem	theorem	NOUN
ejpam-2979	91	20	1	1	NUM
ejpam-2979	91	21	.	.	PUNCT
ejpam-2979	92	1	for	for	ADP
ejpam-2979	92	2	all	all	DET
ejpam-2979	92	3	n	n	NOUN
ejpam-2979	92	4	,	,	PUNCT
ejpam-2979	92	5	m	m	PROPN
ejpam-2979	92	6	∈	∈	PROPN
ejpam-2979	92	7	z	z	NOUN
ejpam-2979	92	8	,	,	PUNCT
ejpam-2979	92	9	we	we	PRON
ejpam-2979	92	10	have	have	AUX
ejpam-2979	92	11	ckukgk(n+m	ckukgk(n+m	ADV
ejpam-2979	92	12	)	)	PUNCT
ejpam-2979	93	1	=	=	SYM
ejpam-2979	93	2	gkngk(m+1	gkngk(m+1	NOUN
ejpam-2979	93	3	)	)	PUNCT
ejpam-2979	93	4	−	−	PROPN
ejpam-2979	94	1	(	(	PUNCT
ejpam-2979	94	2	c2k	c2k	X
ejpam-2979	94	3	(	(	PUNCT
ejpam-2979	94	4	−q)k	−q)k	NOUN
ejpam-2979	94	5	+	+	CCONJ
ejpam-2979	94	6	ckvk	ckvk	VERB
ejpam-2979	94	7	+	+	CCONJ
ejpam-2979	94	8	1	1	X
ejpam-2979	94	9	)	)	PUNCT
ejpam-2979	94	10	gk(n−1)gkm	gk(n−1)gkm	NOUN
ejpam-2979	94	11	.	.	PUNCT
ejpam-2979	95	1	(	(	PUNCT
ejpam-2979	95	2	5	5	X
ejpam-2979	95	3	)	)	PUNCT
ejpam-2979	95	4	proof	proof	NOUN
ejpam-2979	95	5	.	.	PUNCT
ejpam-2979	96	1	after	after	ADP
ejpam-2979	96	2	some	some	DET
ejpam-2979	96	3	simplications,(2	simplications,(2	NOUN
ejpam-2979	96	4	,	,	PUNCT
ejpam-2979	96	5	1)−entries	1)−entries	NUM
ejpam-2979	96	6	of	of	ADP
ejpam-2979	96	7	anam	anam	X
ejpam-2979	96	8	=	=	SYM
ejpam-2979	96	9	an+m	an+m	PROPN
ejpam-2979	96	10	give	give	VERB
ejpam-2979	96	11	the	the	DET
ejpam-2979	96	12	conclusion	conclusion	NOUN
ejpam-2979	96	13	.	.	PUNCT
ejpam-2979	97	1	for	for	ADP
ejpam-2979	97	2	example	example	NOUN
ejpam-2979	97	3	,	,	PUNCT
ejpam-2979	97	4	when	when	SCONJ
ejpam-2979	97	5	n	n	X
ejpam-2979	97	6	=	=	VERB
ejpam-2979	97	7	m	m	VERB
ejpam-2979	97	8	in	in	ADP
ejpam-2979	97	9	(	(	PUNCT
ejpam-2979	97	10	5	5	NUM
ejpam-2979	97	11	)	)	PUNCT
ejpam-2979	97	12	,	,	PUNCT
ejpam-2979	97	13	we	we	PRON
ejpam-2979	97	14	have	have	VERB
ejpam-2979	97	15	ckukg2kn	ckukg2kn	ADJ
ejpam-2979	97	16	=	=	SYM
ejpam-2979	97	17	gkngk(n+1	gkngk(n+1	NOUN
ejpam-2979	97	18	)	)	PUNCT
ejpam-2979	97	19	−	−	PROPN
ejpam-2979	98	1	(	(	PUNCT
ejpam-2979	98	2	c2k	c2k	X
ejpam-2979	98	3	(	(	PUNCT
ejpam-2979	98	4	−q)k	−q)k	NOUN
ejpam-2979	98	5	+	+	CCONJ
ejpam-2979	98	6	ckvk	ckvk	VERB
ejpam-2979	98	7	+	+	CCONJ
ejpam-2979	98	8	1	1	NUM
ejpam-2979	98	9	)	)	PUNCT
ejpam-2979	98	10	gkngk(n−1	gkngk(n−1	PROPN
ejpam-2979	98	11	)	)	PUNCT
ejpam-2979	98	12	,	,	PUNCT
ejpam-2979	98	13	or	or	CCONJ
ejpam-2979	98	14	ckukhkn	ckukhkn	NOUN
ejpam-2979	98	15	=	=	SYM
ejpam-2979	98	16	gk(n+1	gk(n+1	NOUN
ejpam-2979	98	17	)	)	PUNCT
ejpam-2979	98	18	−	−	PROPN
ejpam-2979	99	1	(	(	PUNCT
ejpam-2979	99	2	c2k	c2k	X
ejpam-2979	99	3	(	(	PUNCT
ejpam-2979	99	4	−q)k	−q)k	NOUN
ejpam-2979	99	5	+	+	CCONJ
ejpam-2979	99	6	ckvk	ckvk	VERB
ejpam-2979	99	7	+	+	CCONJ
ejpam-2979	99	8	1	1	X
ejpam-2979	99	9	)	)	PUNCT
ejpam-2979	99	10	gk(n−1	gk(n−1	PROPN
ejpam-2979	99	11	)	)	PUNCT
ejpam-2979	99	12	.	.	PUNCT
ejpam-2979	100	1	theorem	theorem	NOUN
ejpam-2979	100	2	2	2	NUM
ejpam-2979	100	3	.	.	X
ejpam-2979	100	4	for	for	ADP
ejpam-2979	100	5	all	all	DET
ejpam-2979	100	6	n	n	PRON
ejpam-2979	100	7	∈	∈	PROPN
ejpam-2979	100	8	z	z	NOUN
ejpam-2979	100	9	,	,	PUNCT
ejpam-2979	100	10	we	we	PRON
ejpam-2979	100	11	have	have	VERB
ejpam-2979	100	12	ckuk	ckuk	NOUN
ejpam-2979	100	13	(	(	PUNCT
ejpam-2979	100	14	gk(2n+1	gk(2n+1	NOUN
ejpam-2979	100	15	)	)	PUNCT
ejpam-2979	100	16	+	+	CCONJ
ejpam-2979	100	17	gk(2n−1	gk(2n−1	NOUN
ejpam-2979	100	18	)	)	PUNCT
ejpam-2979	100	19	)	)	PUNCT
ejpam-2979	101	1	=	=	SYM
ejpam-2979	101	2	g2k(n+1	g2k(n+1	NOUN
ejpam-2979	101	3	)	)	PUNCT
ejpam-2979	101	4	−	−	PROPN
ejpam-2979	101	5	(	(	PUNCT
ejpam-2979	101	6	c2k	c2k	X
ejpam-2979	101	7	(	(	PUNCT
ejpam-2979	101	8	−q)k	−q)k	NOUN
ejpam-2979	101	9	+	+	CCONJ
ejpam-2979	101	10	ckvk	ckvk	NOUN
ejpam-2979	101	11	)	)	PUNCT
ejpam-2979	101	12	g2kn	g2kn	VERB
ejpam-2979	101	13	−	−	PROPN
ejpam-2979	102	1	(	(	PUNCT
ejpam-2979	102	2	c2k	c2k	X
ejpam-2979	102	3	(	(	PUNCT
ejpam-2979	102	4	−q)k	−q)k	NOUN
ejpam-2979	102	5	+	+	CCONJ
ejpam-2979	102	6	ckvk	ckvk	VERB
ejpam-2979	102	7	+	+	CCONJ
ejpam-2979	102	8	1	1	X
ejpam-2979	102	9	)	)	PUNCT
ejpam-2979	102	10	g2k(n−1	g2k(n−1	PROPN
ejpam-2979	102	11	)	)	PUNCT
ejpam-2979	102	12	,	,	PUNCT
ejpam-2979	102	13	ckuk	ckuk	NOUN
ejpam-2979	102	14	(	(	PUNCT
ejpam-2979	102	15	gk(2n+1	gk(2n+1	NOUN
ejpam-2979	102	16	)	)	PUNCT
ejpam-2979	102	17	−	−	PROPN
ejpam-2979	102	18	gk(2n−1	gk(2n−1	PROPN
ejpam-2979	102	19	)	)	PUNCT
ejpam-2979	102	20	)	)	PUNCT
ejpam-2979	103	1	=	=	SYM
ejpam-2979	103	2	g2k(n+1	g2k(n+1	NOUN
ejpam-2979	103	3	)	)	PUNCT
ejpam-2979	103	4	−	−	PROPN
ejpam-2979	103	5	(	(	PUNCT
ejpam-2979	103	6	c2k	c2k	X
ejpam-2979	103	7	(	(	PUNCT
ejpam-2979	103	8	−q)k	−q)k	NOUN
ejpam-2979	103	9	+	+	CCONJ
ejpam-2979	103	10	ckvk	ckvk	VERB
ejpam-2979	103	11	+	+	CCONJ
ejpam-2979	103	12	2	2	NUM
ejpam-2979	103	13	)	)	PUNCT
ejpam-2979	103	14	g2kn	g2kn	PUNCT
ejpam-2979	104	1	+	+	CCONJ
ejpam-2979	104	2	(	(	PUNCT
ejpam-2979	104	3	c2k	c2k	X
ejpam-2979	104	4	(	(	PUNCT
ejpam-2979	104	5	−q)k	−q)k	NOUN
ejpam-2979	104	6	+	+	CCONJ
ejpam-2979	104	7	ckvk	ckvk	VERB
ejpam-2979	104	8	+	+	CCONJ
ejpam-2979	104	9	1	1	X
ejpam-2979	104	10	)	)	PUNCT
ejpam-2979	104	11	g2k(n−1	g2k(n−1	PROPN
ejpam-2979	104	12	)	)	PUNCT
ejpam-2979	104	13	.	.	PUNCT
ejpam-2979	105	1	proof	proof	NOUN
ejpam-2979	105	2	.	.	PUNCT
ejpam-2979	106	1	considering	consider	VERB
ejpam-2979	106	2	the	the	DET
ejpam-2979	106	3	(	(	PUNCT
ejpam-2979	106	4	1	1	NUM
ejpam-2979	106	5	,	,	PUNCT
ejpam-2979	106	6	1	1	NUM
ejpam-2979	106	7	)	)	PUNCT
ejpam-2979	106	8	and	and	CCONJ
ejpam-2979	106	9	(	(	PUNCT
ejpam-2979	106	10	2	2	NUM
ejpam-2979	106	11	,	,	PUNCT
ejpam-2979	106	12	2)−entries	2)−entries	NUM
ejpam-2979	106	13	of	of	ADP
ejpam-2979	106	14	the	the	DET
ejpam-2979	106	15	matrix	matrix	NOUN
ejpam-2979	106	16	equation	equation	NOUN
ejpam-2979	106	17	a2n	a2n	VERB
ejpam-2979	106	18	=	=	PRON
ejpam-2979	106	19	(	(	PUNCT
ejpam-2979	106	20	an)2	an)2	PROPN
ejpam-2979	106	21	,	,	PUNCT
ejpam-2979	106	22	we	we	PRON
ejpam-2979	106	23	have	have	VERB
ejpam-2979	106	24	g2k(n+1	g2k(n+1	NOUN
ejpam-2979	106	25	)	)	PUNCT
ejpam-2979	106	26	−	−	PROPN
ejpam-2979	107	1	(	(	PUNCT
ejpam-2979	107	2	c2k	c2k	X
ejpam-2979	107	3	(	(	PUNCT
ejpam-2979	107	4	−q)k	−q)k	NOUN
ejpam-2979	107	5	+	+	CCONJ
ejpam-2979	107	6	ckvk	ckvk	VERB
ejpam-2979	107	7	+	+	CCONJ
ejpam-2979	107	8	1	1	NUM
ejpam-2979	107	9	)	)	PUNCT
ejpam-2979	107	10	g2kn	g2kn	PUNCT
ejpam-2979	107	11	=	=	SYM
ejpam-2979	107	12	ckukgk(2n+1	ckukgk(2n+1	NOUN
ejpam-2979	107	13	)	)	PUNCT
ejpam-2979	107	14	,	,	PUNCT
ejpam-2979	107	15	(	(	PUNCT
ejpam-2979	107	16	6	6	NUM
ejpam-2979	107	17	)	)	PUNCT
ejpam-2979	107	18	g2kn	g2kn	NOUN
ejpam-2979	107	19	−	−	PROPN
ejpam-2979	108	1	(	(	PUNCT
ejpam-2979	108	2	c2k	c2k	X
ejpam-2979	108	3	(	(	PUNCT
ejpam-2979	108	4	−q)k	−q)k	NOUN
ejpam-2979	108	5	+	+	CCONJ
ejpam-2979	108	6	ckvk	ckvk	VERB
ejpam-2979	108	7	+	+	CCONJ
ejpam-2979	108	8	1	1	X
ejpam-2979	108	9	)	)	PUNCT
ejpam-2979	108	10	g2k(n−1	g2k(n−1	PROPN
ejpam-2979	108	11	)	)	PUNCT
ejpam-2979	108	12	=	=	PUNCT
ejpam-2979	108	13	ckukgk(2n−1	ckukgk(2n−1	ADJ
ejpam-2979	108	14	)	)	PUNCT
ejpam-2979	108	15	.	.	PUNCT
ejpam-2979	109	1	(	(	PUNCT
ejpam-2979	109	2	7	7	X
ejpam-2979	109	3	)	)	PUNCT
ejpam-2979	109	4	by	by	ADP
ejpam-2979	109	5	adding	add	VERB
ejpam-2979	109	6	and	and	CCONJ
ejpam-2979	109	7	substracting	substracting	NOUN
ejpam-2979	109	8	of	of	ADP
ejpam-2979	109	9	(	(	PUNCT
ejpam-2979	109	10	6	6	NUM
ejpam-2979	109	11	)	)	PUNCT
ejpam-2979	109	12	and	and	CCONJ
ejpam-2979	109	13	(	(	PUNCT
ejpam-2979	109	14	7	7	X
ejpam-2979	109	15	)	)	PUNCT
ejpam-2979	109	16	side	side	NOUN
ejpam-2979	109	17	by	by	ADP
ejpam-2979	109	18	side	side	NOUN
ejpam-2979	109	19	,	,	PUNCT
ejpam-2979	109	20	we	we	PRON
ejpam-2979	109	21	have	have	VERB
ejpam-2979	109	22	the	the	DET
ejpam-2979	109	23	conclusion	conclusion	NOUN
ejpam-2979	109	24	.	.	PUNCT
ejpam-2979	110	1	theorem	theorem	NOUN
ejpam-2979	110	2	3	3	NUM
ejpam-2979	110	3	.	.	NOUN
ejpam-2979	110	4	for	for	ADP
ejpam-2979	110	5	n	n	PROPN
ejpam-2979	110	6	>	>	X
ejpam-2979	110	7	0	0	NUM
ejpam-2979	110	8	,	,	PUNCT
ejpam-2979	110	9	we	we	PRON
ejpam-2979	110	10	have	have	VERB
ejpam-2979	110	11	gkn	gkn	NOUN
ejpam-2979	110	12	=	=	SYM
ejpam-2979	110	13	n∑	n∑	NOUN
ejpam-2979	110	14	t=0	t=0	PROPN
ejpam-2979	110	15	(	(	PUNCT
ejpam-2979	110	16	n	n	NOUN
ejpam-2979	110	17	t	t	NOUN
ejpam-2979	110	18	)	)	PUNCT
ejpam-2979	110	19	(	(	PUNCT
ejpam-2979	110	20	ckvk	ckvk	VERB
ejpam-2979	110	21	+	+	CCONJ
ejpam-2979	110	22	2	2	NUM
ejpam-2979	110	23	)	)	PUNCT
ejpam-2979	110	24	t	t	NOUN
ejpam-2979	110	25	(	(	PUNCT
ejpam-2979	110	26	−1)n−t	−1)n−t	PROPN
ejpam-2979	110	27	(	(	PUNCT
ejpam-2979	110	28	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	110	29	+	+	CCONJ
ejpam-2979	110	30	ckvk	ckvk	NOUN
ejpam-2979	110	31	+	+	CCONJ
ejpam-2979	110	32	1	1	NUM
ejpam-2979	110	33	)	)	PUNCT
ejpam-2979	110	34	−n+t	−n+t	NOUN
ejpam-2979	110	35	gk(n−t	gk(n−t	PROPN
ejpam-2979	110	36	)	)	PUNCT
ejpam-2979	110	37	.	.	PUNCT
ejpam-2979	111	1	proof	proof	NOUN
ejpam-2979	111	2	.	.	PUNCT
ejpam-2979	112	1	from	from	ADP
ejpam-2979	112	2	the	the	DET
ejpam-2979	112	3	matrix	matrix	NOUN
ejpam-2979	112	4	relation	relation	NOUN
ejpam-2979	112	5	,	,	PUNCT
ejpam-2979	112	6	we	we	PRON
ejpam-2979	112	7	write	write	VERB
ejpam-2979	112	8	an	an	DET
ejpam-2979	112	9	=	=	X
ejpam-2979	112	10	(	(	PUNCT
ejpam-2979	112	11	(	(	PUNCT
ejpam-2979	112	12	ckvk	ckvk	VERB
ejpam-2979	112	13	+	+	CCONJ
ejpam-2979	112	14	2	2	X
ejpam-2979	112	15	)	)	PUNCT
ejpam-2979	113	1	i	i	PRON
ejpam-2979	113	2	−	−	PROPN
ejpam-2979	114	1	(	(	PUNCT
ejpam-2979	114	2	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	114	3	+	+	CCONJ
ejpam-2979	114	4	ckvk	ckvk	NOUN
ejpam-2979	114	5	+	+	CCONJ
ejpam-2979	114	6	1	1	X
ejpam-2979	114	7	)	)	PUNCT
ejpam-2979	114	8	a−1	a−1	PROPN
ejpam-2979	114	9	)	)	PUNCT
ejpam-2979	114	10	n	n	PROPN
ejpam-2979	114	11	=	=	SYM
ejpam-2979	114	12	n∑	n∑	PROPN
ejpam-2979	114	13	t=0	t=0	PROPN
ejpam-2979	114	14	(	(	PUNCT
ejpam-2979	114	15	n	n	NOUN
ejpam-2979	114	16	t	t	NOUN
ejpam-2979	114	17	)	)	PUNCT
ejpam-2979	114	18	(	(	PUNCT
ejpam-2979	114	19	ckvk	ckvk	VERB
ejpam-2979	114	20	+	+	CCONJ
ejpam-2979	114	21	2	2	NUM
ejpam-2979	114	22	)	)	PUNCT
ejpam-2979	114	23	t	t	NOUN
ejpam-2979	114	24	(	(	PUNCT
ejpam-2979	114	25	c2k(−q)k+1	c2k(−q)k+1	NOUN
ejpam-2979	114	26	−	−	PROPN
ejpam-2979	114	27	ckvk	ckvk	NOUN
ejpam-2979	114	28	−	−	PROPN
ejpam-2979	114	29	1	1	NUM
ejpam-2979	114	30	)	)	PUNCT
ejpam-2979	114	31	n−t	n−t	ADJ
ejpam-2979	114	32	a−(n−t	a−(n−t	NOUN
ejpam-2979	114	33	)	)	PUNCT
ejpam-2979	114	34	.	.	PUNCT
ejpam-2979	115	1	(	(	PUNCT
ejpam-2979	115	2	8)	8)	NUM
ejpam-2979	115	3	then	then	ADV
ejpam-2979	115	4	equating	equate	VERB
ejpam-2979	115	5	(	(	PUNCT
ejpam-2979	115	6	2	2	NUM
ejpam-2979	115	7	,	,	PUNCT
ejpam-2979	115	8	1)−entries	1)−entries	NUM
ejpam-2979	115	9	of	of	ADP
ejpam-2979	115	10	the	the	DET
ejpam-2979	115	11	equality	equality	NOUN
ejpam-2979	115	12	(	(	PUNCT
ejpam-2979	115	13	8)	8)	NUM
ejpam-2979	115	14	,	,	PUNCT
ejpam-2979	115	15	we	we	PRON
ejpam-2979	115	16	get	get	VERB
ejpam-2979	115	17	gkn	gkn	ADJ
ejpam-2979	115	18	=	=	SYM
ejpam-2979	115	19	n∑	n∑	NOUN
ejpam-2979	115	20	t=0	t=0	PROPN
ejpam-2979	115	21	(	(	PUNCT
ejpam-2979	115	22	n	n	NOUN
ejpam-2979	115	23	t	t	NOUN
ejpam-2979	115	24	)	)	PUNCT
ejpam-2979	115	25	(	(	PUNCT
ejpam-2979	115	26	ckvk	ckvk	VERB
ejpam-2979	115	27	+	+	CCONJ
ejpam-2979	115	28	2	2	NUM
ejpam-2979	115	29	)	)	PUNCT
ejpam-2979	115	30	t	t	NOUN
ejpam-2979	115	31	(	(	PUNCT
ejpam-2979	115	32	−1)n−t	−1)n−t	PROPN
ejpam-2979	115	33	(	(	PUNCT
ejpam-2979	115	34	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	115	35	+	+	CCONJ
ejpam-2979	115	36	ckvk	ckvk	NOUN
ejpam-2979	115	37	+	+	CCONJ
ejpam-2979	115	38	1	1	NUM
ejpam-2979	115	39	)	)	PUNCT
ejpam-2979	115	40	−n+t	−n+t	NOUN
ejpam-2979	115	41	gk(n−t	gk(n−t	PROPN
ejpam-2979	115	42	)	)	PUNCT
ejpam-2979	115	43	.	.	PUNCT
ejpam-2979	116	1	n.	n.	PROPN
ejpam-2979	116	2	ömür	ömür	PROPN
ejpam-2979	116	3	,	,	PUNCT
ejpam-2979	116	4	c.	c.	PROPN
ejpam-2979	116	5	d.	d.	PROPN
ejpam-2979	116	6	şener	şener	PROPN
ejpam-2979	116	7	/	/	SYM
ejpam-2979	116	8	eur	eur	PROPN
ejpam-2979	116	9	.	.	PUNCT
ejpam-2979	117	1	j.	j.	PROPN
ejpam-2979	117	2	pure	pure	PROPN
ejpam-2979	117	3	appl	appl	PROPN
ejpam-2979	117	4	.	.	PROPN
ejpam-2979	117	5	math	math	PROPN
ejpam-2979	117	6	,	,	PUNCT
ejpam-2979	117	7	10	10	NUM
ejpam-2979	117	8	(	(	PUNCT
ejpam-2979	117	9	3	3	NUM
ejpam-2979	117	10	)	)	PUNCT
ejpam-2979	117	11	(	(	PUNCT
ejpam-2979	117	12	2017	2017	NUM
ejpam-2979	117	13	)	)	PUNCT
ejpam-2979	117	14	,	,	PUNCT
ejpam-2979	117	15	506	506	NUM
ejpam-2979	117	16	-	-	SYM
ejpam-2979	117	17	515	515	NUM
ejpam-2979	117	18	512	512	NUM
ejpam-2979	117	19	theorem	theorem	NOUN
ejpam-2979	117	20	4	4	NUM
ejpam-2979	117	21	.	.	NOUN
ejpam-2979	117	22	for	for	ADP
ejpam-2979	117	23	n	n	PROPN
ejpam-2979	117	24	>	>	X
ejpam-2979	117	25	0	0	NUM
ejpam-2979	117	26	,	,	PUNCT
ejpam-2979	117	27	we	we	PRON
ejpam-2979	117	28	have	have	AUX
ejpam-2979	117	29	2n∑	2n∑	NUM
ejpam-2979	117	30	i=0	i=0	PROPN
ejpam-2979	117	31	(	(	PUNCT
ejpam-2979	117	32	2n	2n	NUM
ejpam-2979	117	33	i	i	NOUN
ejpam-2979	117	34	)	)	PUNCT
ejpam-2979	117	35	(	(	PUNCT
ejpam-2979	117	36	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	117	37	+	+	CCONJ
ejpam-2979	117	38	ckvk	ckvk	NOUN
ejpam-2979	117	39	+	+	CCONJ
ejpam-2979	117	40	1	1	NUM
ejpam-2979	117	41	)	)	PUNCT
ejpam-2979	117	42	2n−i	2n−i	NOUN
ejpam-2979	117	43	gk(2i+1	gk(2i+1	NOUN
ejpam-2979	117	44	)	)	PUNCT
ejpam-2979	118	1	=	=	PRON
ejpam-2979	118	2	(	(	PUNCT
ejpam-2979	118	3	ckvk	ckvk	VERB
ejpam-2979	118	4	+	+	CCONJ
ejpam-2979	118	5	2	2	NUM
ejpam-2979	118	6	)	)	PUNCT
ejpam-2979	118	7	2n	2n	NUM
ejpam-2979	118	8	gk(2n+1	gk(2n+1	NOUN
ejpam-2979	118	9	)	)	PUNCT
ejpam-2979	118	10	,	,	PUNCT
ejpam-2979	118	11	2n∑	2n∑	PROPN
ejpam-2979	118	12	i=0	i=0	PROPN
ejpam-2979	118	13	(	(	PUNCT
ejpam-2979	118	14	2n	2n	NUM
ejpam-2979	118	15	i	i	NOUN
ejpam-2979	118	16	)	)	PUNCT
ejpam-2979	118	17	(	(	PUNCT
ejpam-2979	118	18	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	118	19	+	+	CCONJ
ejpam-2979	118	20	ckvk	ckvk	NOUN
ejpam-2979	118	21	+	+	CCONJ
ejpam-2979	118	22	1	1	NUM
ejpam-2979	118	23	)	)	PUNCT
ejpam-2979	118	24	2n−i	2n−i	NOUN
ejpam-2979	118	25	g2ki	g2ki	NOUN
ejpam-2979	118	26	=	=	SYM
ejpam-2979	118	27	(	(	PUNCT
ejpam-2979	118	28	ckvk	ckvk	VERB
ejpam-2979	118	29	+	+	CCONJ
ejpam-2979	118	30	2	2	NUM
ejpam-2979	118	31	)	)	PUNCT
ejpam-2979	118	32	2n	2n	NUM
ejpam-2979	118	33	g2kn	g2kn	PUNCT
ejpam-2979	118	34	.	.	PUNCT
ejpam-2979	119	1	proof	proof	NOUN
ejpam-2979	119	2	.	.	PUNCT
ejpam-2979	120	1	the	the	DET
ejpam-2979	120	2	matrix	matrix	NOUN
ejpam-2979	120	3	a2	a2	PROPN
ejpam-2979	120	4	is	be	AUX
ejpam-2979	120	5	[	[	PUNCT
ejpam-2979	120	6	(	(	PUNCT
ejpam-2979	120	7	ckvk	ckvk	VERB
ejpam-2979	120	8	+	+	CCONJ
ejpam-2979	120	9	2	2	NUM
ejpam-2979	120	10	)	)	SYM
ejpam-2979	120	11	2	2	NUM
ejpam-2979	120	12	+	+	NUM
ejpam-2979	120	13	qk(−1)k+1c2k	qk(−1)k+1c2k	NOUN
ejpam-2979	120	14	−	−	NOUN
ejpam-2979	120	15	ckvk	ckvk	VERB
ejpam-2979	120	16	−	−	PROPN
ejpam-2979	120	17	1	1	NUM
ejpam-2979	120	18	(	(	PUNCT
ejpam-2979	120	19	ckvk	ckvk	VERB
ejpam-2979	120	20	+	+	CCONJ
ejpam-2979	120	21	2	2	NUM
ejpam-2979	120	22	)	)	PUNCT
ejpam-2979	120	23	(	(	PUNCT
ejpam-2979	120	24	qk(−1)k+1c2k	qk(−1)k+1c2k	ADV
ejpam-2979	120	25	−	−	PRON
ejpam-2979	120	26	ckvk	ckvk	VERB
ejpam-2979	120	27	−	−	PROPN
ejpam-2979	120	28	1	1	NUM
ejpam-2979	120	29	)	)	PUNCT
ejpam-2979	120	30	ckvk	ckvk	NOUN
ejpam-2979	121	1	+	+	CCONJ
ejpam-2979	121	2	2	2	NUM
ejpam-2979	121	3	qk(−1)k+1c2k	qk(−1)k+1c2k	NOUN
ejpam-2979	121	4	−	−	NOUN
ejpam-2979	121	5	ckvk	ckvk	VERB
ejpam-2979	121	6	−	−	PROPN
ejpam-2979	121	7	1	1	NUM
ejpam-2979	121	8	]	]	PUNCT
ejpam-2979	121	9	and	and	CCONJ
ejpam-2979	121	10	the	the	DET
ejpam-2979	121	11	characteristic	characteristic	ADJ
ejpam-2979	121	12	equation	equation	NOUN
ejpam-2979	121	13	for	for	ADP
ejpam-2979	121	14	a2	a2	PROPN
ejpam-2979	121	15	is	be	AUX
ejpam-2979	121	16	λ	λ	NOUN
ejpam-2979	121	17	(	(	PUNCT
ejpam-2979	121	18	ckvk	ckvk	VERB
ejpam-2979	121	19	+	+	CCONJ
ejpam-2979	121	20	2	2	NUM
ejpam-2979	121	21	)	)	SYM
ejpam-2979	121	22	2	2	NUM
ejpam-2979	121	23	=	=	SYM
ejpam-2979	121	24	(	(	PUNCT
ejpam-2979	121	25	λ+	λ+	X
ejpam-2979	121	26	(	(	PUNCT
ejpam-2979	121	27	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	121	28	+	+	CCONJ
ejpam-2979	121	29	ckvk	ckvk	NOUN
ejpam-2979	121	30	+	+	CCONJ
ejpam-2979	121	31	1	1	NUM
ejpam-2979	121	32	)	)	PUNCT
ejpam-2979	121	33	)	)	PUNCT
ejpam-2979	121	34	2	2	NUM
ejpam-2979	121	35	.	.	PUNCT
ejpam-2979	122	1	(	(	PUNCT
ejpam-2979	122	2	9	9	NUM
ejpam-2979	122	3	)	)	PUNCT
ejpam-2979	122	4	from	from	ADP
ejpam-2979	122	5	the	the	DET
ejpam-2979	122	6	caley	caley	PROPN
ejpam-2979	122	7	-	-	PUNCT
ejpam-2979	122	8	hamilton	hamilton	PROPN
ejpam-2979	122	9	theorem	theorem	PROPN
ejpam-2979	122	10	for	for	ADP
ejpam-2979	122	11	a2	a2	PROPN
ejpam-2979	122	12	,	,	PUNCT
ejpam-2979	122	13	we	we	PRON
ejpam-2979	122	14	have	have	VERB
ejpam-2979	122	15	a2	a2	PROPN
ejpam-2979	122	16	(	(	PUNCT
ejpam-2979	122	17	ckvk	ckvk	VERB
ejpam-2979	122	18	+	+	CCONJ
ejpam-2979	122	19	2	2	NUM
ejpam-2979	122	20	)	)	SYM
ejpam-2979	122	21	2	2	NUM
ejpam-2979	122	22	=	=	SYM
ejpam-2979	122	23	(	(	PUNCT
ejpam-2979	122	24	a2	a2	PROPN
ejpam-2979	122	25	+	+	CCONJ
ejpam-2979	122	26	(	(	PUNCT
ejpam-2979	122	27	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	122	28	+	+	CCONJ
ejpam-2979	122	29	ckvk	ckvk	NOUN
ejpam-2979	122	30	+	+	CCONJ
ejpam-2979	122	31	1	1	NUM
ejpam-2979	122	32	)	)	PUNCT
ejpam-2979	122	33	i	i	NOUN
ejpam-2979	122	34	)	)	PUNCT
ejpam-2979	122	35	2	2	X
ejpam-2979	122	36	.	.	PUNCT
ejpam-2979	123	1	thus	thus	ADV
ejpam-2979	123	2	a2n	a2n	PROPN
ejpam-2979	123	3	(	(	PUNCT
ejpam-2979	123	4	ckvk	ckvk	VERB
ejpam-2979	123	5	+	+	CCONJ
ejpam-2979	123	6	2	2	NUM
ejpam-2979	123	7	)	)	PUNCT
ejpam-2979	123	8	2n	2n	NUM
ejpam-2979	123	9	=	=	SYM
ejpam-2979	123	10	(	(	PUNCT
ejpam-2979	123	11	a2	a2	PROPN
ejpam-2979	123	12	+	+	CCONJ
ejpam-2979	123	13	(	(	PUNCT
ejpam-2979	123	14	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	123	15	+	+	CCONJ
ejpam-2979	123	16	ckvk	ckvk	NOUN
ejpam-2979	123	17	+	+	CCONJ
ejpam-2979	123	18	1	1	NUM
ejpam-2979	123	19	)	)	PUNCT
ejpam-2979	123	20	i	i	NOUN
ejpam-2979	123	21	)	)	PUNCT
ejpam-2979	123	22	2n	2n	NUM
ejpam-2979	123	23	.	.	PUNCT
ejpam-2979	124	1	by	by	ADP
ejpam-2979	124	2	binomial	binomial	ADJ
ejpam-2979	124	3	theorem	theorem	NOUN
ejpam-2979	124	4	and	and	CCONJ
ejpam-2979	124	5	(	(	PUNCT
ejpam-2979	124	6	3	3	NUM
ejpam-2979	124	7	)	)	PUNCT
ejpam-2979	124	8	,	,	PUNCT
ejpam-2979	124	9	we	we	PRON
ejpam-2979	124	10	have	have	VERB
ejpam-2979	124	11	2n∑	2n∑	PROPN
ejpam-2979	124	12	i=0	i=0	PROPN
ejpam-2979	124	13	(	(	PUNCT
ejpam-2979	124	14	2n	2n	NUM
ejpam-2979	124	15	i	i	NOUN
ejpam-2979	124	16	)	)	PUNCT
ejpam-2979	124	17	(	(	PUNCT
ejpam-2979	124	18	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	124	19	+	+	CCONJ
ejpam-2979	124	20	ckvk	ckvk	NOUN
ejpam-2979	124	21	+	+	CCONJ
ejpam-2979	124	22	1	1	NUM
ejpam-2979	124	23	)	)	PUNCT
ejpam-2979	124	24	2n−i	2n−i	NOUN
ejpam-2979	124	25	a2i	a2i	NOUN
ejpam-2979	125	1	=	=	PUNCT
ejpam-2979	126	1	a2n	a2n	PROPN
ejpam-2979	126	2	(	(	PUNCT
ejpam-2979	126	3	ckvk	ckvk	VERB
ejpam-2979	126	4	+	+	CCONJ
ejpam-2979	126	5	2	2	NUM
ejpam-2979	126	6	)	)	PUNCT
ejpam-2979	126	7	2n	2n	NUM
ejpam-2979	126	8	2n∑	2n∑	PROPN
ejpam-2979	126	9	i=0	i=0	PROPN
ejpam-2979	126	10	(	(	PUNCT
ejpam-2979	126	11	2n	2n	NUM
ejpam-2979	126	12	i	i	NOUN
ejpam-2979	126	13	)	)	PUNCT
ejpam-2979	126	14	(	(	PUNCT
ejpam-2979	126	15	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	126	16	+	+	CCONJ
ejpam-2979	126	17	ckvk	ckvk	NOUN
ejpam-2979	126	18	+	+	CCONJ
ejpam-2979	126	19	1	1	NUM
ejpam-2979	126	20	)	)	PUNCT
ejpam-2979	126	21	2n−i	2n−i	NOUN
ejpam-2979	126	22	[	[	PUNCT
ejpam-2979	126	23	gk(2i+1	gk(2i+1	NOUN
ejpam-2979	126	24	)	)	PUNCT
ejpam-2979	126	25	g2ki	g2ki	X
ejpam-2979	126	26	]	]	PUNCT
ejpam-2979	126	27	=	=	PUNCT
ejpam-2979	126	28	(	(	PUNCT
ejpam-2979	126	29	ckvk	ckvk	VERB
ejpam-2979	126	30	+	+	CCONJ
ejpam-2979	126	31	2	2	NUM
ejpam-2979	126	32	)	)	PUNCT
ejpam-2979	126	33	2n	2n	NUM
ejpam-2979	126	34	[	[	PUNCT
ejpam-2979	126	35	gk(2n+1	gk(2n+1	NOUN
ejpam-2979	126	36	)	)	PUNCT
ejpam-2979	126	37	g2kn	g2kn	PUNCT
ejpam-2979	126	38	]	]	PUNCT
ejpam-2979	126	39	,	,	PUNCT
ejpam-2979	126	40	as	as	SCONJ
ejpam-2979	126	41	claimed	claim	VERB
ejpam-2979	126	42	.	.	PUNCT
ejpam-2979	127	1	theorem	theorem	ADJ
ejpam-2979	127	2	5	5	NUM
ejpam-2979	127	3	.	.	PUNCT
ejpam-2979	127	4	for	for	ADP
ejpam-2979	127	5	n	n	PROPN
ejpam-2979	127	6	>	>	X
ejpam-2979	127	7	0	0	NUM
ejpam-2979	127	8	,	,	PUNCT
ejpam-2979	127	9	we	we	PRON
ejpam-2979	127	10	have	have	VERB
ejpam-2979	127	11	2n∑	2n∑	NUM
ejpam-2979	127	12	i=0	i=0	PROPN
ejpam-2979	127	13	(	(	PUNCT
ejpam-2979	127	14	2n	2n	NUM
ejpam-2979	127	15	i	i	NOUN
ejpam-2979	127	16	)	)	PUNCT
ejpam-2979	127	17	(	(	PUNCT
ejpam-2979	127	18	−1)i	−1)i	X
ejpam-2979	127	19	(	(	PUNCT
ejpam-2979	127	20	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	127	21	+	+	CCONJ
ejpam-2979	127	22	ckvk	ckvk	NOUN
ejpam-2979	127	23	+	+	CCONJ
ejpam-2979	127	24	1	1	NUM
ejpam-2979	127	25	)	)	PUNCT
ejpam-2979	127	26	2n−i	2n−i	NOUN
ejpam-2979	127	27	gk(2i+1	gk(2i+1	NOUN
ejpam-2979	127	28	)	)	PUNCT
ejpam-2979	127	29	=	=	SYM
ejpam-2979	128	1	c2kn	c2kn	PUNCT
ejpam-2979	128	2	(	(	PUNCT
ejpam-2979	128	3	v2k	v2k	X
ejpam-2979	128	4	+	+	X
ejpam-2979	128	5	4qk	4qk	NOUN
ejpam-2979	128	6	(	(	PUNCT
ejpam-2979	128	7	−1)k+1	−1)k+1	PROPN
ejpam-2979	128	8	)	)	PUNCT
ejpam-2979	128	9	n	n	PRON
ejpam-2979	128	10	gk(2n+1	gk(2n+1	NOUN
ejpam-2979	128	11	)	)	PUNCT
ejpam-2979	128	12	,	,	PUNCT
ejpam-2979	128	13	2n∑	2n∑	PROPN
ejpam-2979	128	14	i=0	i=0	PROPN
ejpam-2979	128	15	(	(	PUNCT
ejpam-2979	128	16	2n	2n	NUM
ejpam-2979	128	17	i	i	NOUN
ejpam-2979	128	18	)	)	PUNCT
ejpam-2979	128	19	(	(	PUNCT
ejpam-2979	128	20	−1)i	−1)i	X
ejpam-2979	128	21	(	(	PUNCT
ejpam-2979	128	22	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	128	23	+	+	CCONJ
ejpam-2979	128	24	ckvk	ckvk	NOUN
ejpam-2979	128	25	+	+	CCONJ
ejpam-2979	128	26	1	1	NUM
ejpam-2979	128	27	)	)	PUNCT
ejpam-2979	128	28	2n−i	2n−i	NOUN
ejpam-2979	128	29	g2ki	g2ki	NOUN
ejpam-2979	128	30	=	=	SYM
ejpam-2979	128	31	c2kn	c2kn	PUNCT
ejpam-2979	128	32	(	(	PUNCT
ejpam-2979	128	33	v2k	v2k	X
ejpam-2979	128	34	+	+	X
ejpam-2979	128	35	4qk	4qk	NOUN
ejpam-2979	128	36	(	(	PUNCT
ejpam-2979	128	37	−1)k+1	−1)k+1	PROPN
ejpam-2979	128	38	)	)	PUNCT
ejpam-2979	128	39	n	n	PRON
ejpam-2979	128	40	g2kn	g2kn	PUNCT
ejpam-2979	128	41	.	.	PUNCT
ejpam-2979	129	1	proof	proof	NOUN
ejpam-2979	129	2	.	.	PUNCT
ejpam-2979	130	1	writing	write	VERB
ejpam-2979	130	2	4λ	4λ	PROPN
ejpam-2979	130	3	(	(	PUNCT
ejpam-2979	130	4	qk(−1)k+1c2k	qk(−1)k+1c2k	NOUN
ejpam-2979	130	5	−	−	PRON
ejpam-2979	130	6	ckvk	ckvk	VERB
ejpam-2979	130	7	−	−	PROPN
ejpam-2979	130	8	1	1	NUM
ejpam-2979	130	9	)	)	PUNCT
ejpam-2979	130	10	to	to	ADP
ejpam-2979	130	11	each	each	DET
ejpam-2979	130	12	side	side	NOUN
ejpam-2979	130	13	of	of	ADP
ejpam-2979	130	14	(	(	PUNCT
ejpam-2979	130	15	3	3	NUM
ejpam-2979	130	16	)	)	PUNCT
ejpam-2979	130	17	,	,	PUNCT
ejpam-2979	130	18	we	we	PRON
ejpam-2979	130	19	write	write	VERB
ejpam-2979	130	20	λc2k	λc2k	NOUN
ejpam-2979	130	21	(	(	PUNCT
ejpam-2979	130	22	v2k	v2k	NOUN
ejpam-2979	130	23	−	−	PROPN
ejpam-2979	130	24	4	4	NUM
ejpam-2979	130	25	(	(	PUNCT
ejpam-2979	130	26	−q)k	−q)k	NOUN
ejpam-2979	130	27	)	)	PUNCT
ejpam-2979	130	28	2	2	NUM
ejpam-2979	130	29	=	=	SYM
ejpam-2979	130	30	(	(	PUNCT
ejpam-2979	130	31	λ+	λ+	X
ejpam-2979	130	32	(	(	PUNCT
ejpam-2979	130	33	qk(−1)k+1c2k	qk(−1)k+1c2k	ADV
ejpam-2979	130	34	−	−	PRON
ejpam-2979	130	35	ckvk	ckvk	VERB
ejpam-2979	130	36	−	−	NOUN
ejpam-2979	130	37	1	1	NUM
ejpam-2979	130	38	)	)	PUNCT
ejpam-2979	130	39	)	)	PUNCT
ejpam-2979	130	40	2	2	NUM
ejpam-2979	130	41	.	.	PUNCT
ejpam-2979	131	1	(	(	PUNCT
ejpam-2979	131	2	10	10	NUM
ejpam-2979	131	3	)	)	PUNCT
ejpam-2979	131	4	similarly	similarly	ADV
ejpam-2979	131	5	,	,	PUNCT
ejpam-2979	131	6	using	use	VERB
ejpam-2979	131	7	(	(	PUNCT
ejpam-2979	131	8	10	10	NUM
ejpam-2979	131	9	)	)	PUNCT
ejpam-2979	131	10	,	,	PUNCT
ejpam-2979	131	11	as	as	ADP
ejpam-2979	131	12	the	the	DET
ejpam-2979	131	13	proof	proof	NOUN
ejpam-2979	131	14	of	of	ADP
ejpam-2979	131	15	theorem	theorem	NOUN
ejpam-2979	131	16	1	1	NUM
ejpam-2979	131	17	,	,	PUNCT
ejpam-2979	131	18	the	the	DET
ejpam-2979	131	19	proof	proof	NOUN
ejpam-2979	131	20	is	be	AUX
ejpam-2979	131	21	completed	complete	VERB
ejpam-2979	131	22	.	.	PUNCT
ejpam-2979	132	1	n.	n.	PROPN
ejpam-2979	132	2	ömür	ömür	PROPN
ejpam-2979	132	3	,	,	PUNCT
ejpam-2979	132	4	c.	c.	PROPN
ejpam-2979	132	5	d.	d.	PROPN
ejpam-2979	132	6	şener	şener	PROPN
ejpam-2979	132	7	/	/	SYM
ejpam-2979	132	8	eur	eur	PROPN
ejpam-2979	132	9	.	.	PUNCT
ejpam-2979	133	1	j.	j.	PROPN
ejpam-2979	133	2	pure	pure	PROPN
ejpam-2979	133	3	appl	appl	PROPN
ejpam-2979	133	4	.	.	PROPN
ejpam-2979	133	5	math	math	PROPN
ejpam-2979	133	6	,	,	PUNCT
ejpam-2979	133	7	10	10	NUM
ejpam-2979	133	8	(	(	PUNCT
ejpam-2979	133	9	3	3	NUM
ejpam-2979	133	10	)	)	PUNCT
ejpam-2979	133	11	(	(	PUNCT
ejpam-2979	133	12	2017	2017	NUM
ejpam-2979	133	13	)	)	PUNCT
ejpam-2979	133	14	,	,	PUNCT
ejpam-2979	133	15	506	506	NUM
ejpam-2979	133	16	-	-	SYM
ejpam-2979	133	17	515	515	NUM
ejpam-2979	133	18	513	513	NUM
ejpam-2979	133	19	theorem	theorem	VERB
ejpam-2979	133	20	6	6	NUM
ejpam-2979	133	21	.	.	PUNCT
ejpam-2979	133	22	for	for	ADP
ejpam-2979	133	23	n	n	PROPN
ejpam-2979	133	24	>	>	X
ejpam-2979	133	25	0	0	NUM
ejpam-2979	133	26	,	,	PUNCT
ejpam-2979	133	27	we	we	PRON
ejpam-2979	133	28	have	have	VERB
ejpam-2979	133	29	2n∑	2n∑	NUM
ejpam-2979	133	30	i=0	i=0	PROPN
ejpam-2979	133	31	(	(	PUNCT
ejpam-2979	133	32	2n	2n	NUM
ejpam-2979	133	33	i	i	NOUN
ejpam-2979	133	34	)	)	PUNCT
ejpam-2979	133	35	(	(	PUNCT
ejpam-2979	133	36	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	133	37	+	+	CCONJ
ejpam-2979	133	38	ckvk	ckvk	NOUN
ejpam-2979	134	1	+	+	CCONJ
ejpam-2979	134	2	1	1	NUM
ejpam-2979	134	3	)	)	PUNCT
ejpam-2979	134	4	i	i	PRON
ejpam-2979	134	5	gk(−2i+1	gk(−2i+1	VERB
ejpam-2979	134	6	)	)	PUNCT
ejpam-2979	134	7	=	=	SYM
ejpam-2979	134	8	(	(	PUNCT
ejpam-2979	134	9	ckvk	ckvk	VERB
ejpam-2979	134	10	+	+	CCONJ
ejpam-2979	134	11	2	2	NUM
ejpam-2979	134	12	)	)	PUNCT
ejpam-2979	134	13	2n	2n	NUM
ejpam-2979	134	14	gk(−2n+1	gk(−2n+1	NOUN
ejpam-2979	134	15	)	)	PUNCT
ejpam-2979	134	16	,	,	PUNCT
ejpam-2979	134	17	2n∑	2n∑	PROPN
ejpam-2979	134	18	i=0	i=0	PROPN
ejpam-2979	134	19	(	(	PUNCT
ejpam-2979	134	20	2n	2n	NUM
ejpam-2979	134	21	i	i	NOUN
ejpam-2979	134	22	)	)	PUNCT
ejpam-2979	134	23	(	(	PUNCT
ejpam-2979	134	24	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	134	25	+	+	CCONJ
ejpam-2979	134	26	ckvk	ckvk	NOUN
ejpam-2979	135	1	+	+	CCONJ
ejpam-2979	135	2	1	1	NUM
ejpam-2979	135	3	)	)	PUNCT
ejpam-2979	135	4	i	i	PRON
ejpam-2979	135	5	g−2ki	g−2ki	NOUN
ejpam-2979	135	6	=	=	PUNCT
ejpam-2979	135	7	(	(	PUNCT
ejpam-2979	135	8	ckvk	ckvk	VERB
ejpam-2979	135	9	+	+	CCONJ
ejpam-2979	135	10	2	2	NUM
ejpam-2979	135	11	)	)	PUNCT
ejpam-2979	135	12	2n	2n	NUM
ejpam-2979	135	13	g−2kn	g−2kn	ADV
ejpam-2979	135	14	.	.	PUNCT
ejpam-2979	136	1	proof	proof	NOUN
ejpam-2979	136	2	.	.	PUNCT
ejpam-2979	137	1	the	the	DET
ejpam-2979	137	2	characteristic	characteristic	ADJ
ejpam-2979	137	3	equation	equation	NOUN
ejpam-2979	137	4	for	for	ADP
ejpam-2979	137	5	a−2	a−2	PROPN
ejpam-2979	137	6	is	be	AUX
ejpam-2979	137	7	(	(	PUNCT
ejpam-2979	137	8	λ	λ	X
ejpam-2979	137	9	(	(	PUNCT
ejpam-2979	137	10	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	137	11	+	+	CCONJ
ejpam-2979	137	12	ckvk	ckvk	NOUN
ejpam-2979	137	13	+	+	CCONJ
ejpam-2979	137	14	1	1	NUM
ejpam-2979	137	15	)	)	PUNCT
ejpam-2979	138	1	+	+	CCONJ
ejpam-2979	138	2	1	1	X
ejpam-2979	138	3	)	)	SYM
ejpam-2979	138	4	2	2	NUM
ejpam-2979	138	5	=	=	SYM
ejpam-2979	138	6	λ	λ	NOUN
ejpam-2979	138	7	(	(	PUNCT
ejpam-2979	138	8	ckvk	ckvk	VERB
ejpam-2979	138	9	+	+	CCONJ
ejpam-2979	138	10	2	2	NUM
ejpam-2979	138	11	)	)	SYM
ejpam-2979	138	12	2	2	NUM
ejpam-2979	138	13	.	.	PUNCT
ejpam-2979	139	1	from	from	ADP
ejpam-2979	139	2	the	the	DET
ejpam-2979	139	3	caley	caley	PROPN
ejpam-2979	139	4	-	-	PUNCT
ejpam-2979	139	5	hamilton	hamilton	PROPN
ejpam-2979	139	6	theorem	theorem	PROPN
ejpam-2979	139	7	for	for	ADP
ejpam-2979	139	8	a−2	a−2	PROPN
ejpam-2979	139	9	,	,	PUNCT
ejpam-2979	139	10	we	we	PRON
ejpam-2979	139	11	have	have	VERB
ejpam-2979	139	12	(	(	PUNCT
ejpam-2979	139	13	a−2	a−2	PROPN
ejpam-2979	139	14	(	(	PUNCT
ejpam-2979	139	15	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	139	16	+	+	CCONJ
ejpam-2979	139	17	ckvk	ckvk	NOUN
ejpam-2979	140	1	+	+	CCONJ
ejpam-2979	140	2	1	1	NUM
ejpam-2979	140	3	)	)	PUNCT
ejpam-2979	140	4	+	+	CCONJ
ejpam-2979	140	5	1	1	NUM
ejpam-2979	140	6	)	)	SYM
ejpam-2979	140	7	2	2	NUM
ejpam-2979	140	8	=	=	SYM
ejpam-2979	140	9	(	(	PUNCT
ejpam-2979	140	10	ckvk	ckvk	VERB
ejpam-2979	140	11	+	+	CCONJ
ejpam-2979	141	1	2	2	NUM
ejpam-2979	141	2	)	)	SYM
ejpam-2979	141	3	2	2	NUM
ejpam-2979	141	4	a−2	a−2	PROPN
ejpam-2979	141	5	.	.	PUNCT
ejpam-2979	142	1	thus	thus	ADV
ejpam-2979	142	2	(	(	PUNCT
ejpam-2979	142	3	a−2	a−2	PROPN
ejpam-2979	142	4	(	(	PUNCT
ejpam-2979	142	5	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	142	6	+	+	CCONJ
ejpam-2979	142	7	ckvk	ckvk	NOUN
ejpam-2979	142	8	+	+	CCONJ
ejpam-2979	142	9	1	1	NUM
ejpam-2979	142	10	)	)	PUNCT
ejpam-2979	142	11	+	+	CCONJ
ejpam-2979	142	12	1	1	NUM
ejpam-2979	142	13	)	)	PUNCT
ejpam-2979	142	14	2n	2n	NUM
ejpam-2979	143	1	=	=	PUNCT
ejpam-2979	143	2	(	(	PUNCT
ejpam-2979	143	3	ckvk	ckvk	VERB
ejpam-2979	143	4	+	+	CCONJ
ejpam-2979	143	5	2	2	NUM
ejpam-2979	143	6	)	)	PUNCT
ejpam-2979	143	7	2n	2n	NUM
ejpam-2979	143	8	a−2n	a−2n	PROPN
ejpam-2979	143	9	.	.	PUNCT
ejpam-2979	144	1	by	by	ADP
ejpam-2979	144	2	binomial	binomial	ADJ
ejpam-2979	144	3	theorem	theorem	NOUN
ejpam-2979	144	4	and	and	CCONJ
ejpam-2979	144	5	(	(	PUNCT
ejpam-2979	144	6	4	4	NUM
ejpam-2979	144	7	)	)	PUNCT
ejpam-2979	144	8	,	,	PUNCT
ejpam-2979	144	9	we	we	PRON
ejpam-2979	144	10	have	have	VERB
ejpam-2979	144	11	2n∑	2n∑	PROPN
ejpam-2979	144	12	i=0	i=0	PROPN
ejpam-2979	144	13	(	(	PUNCT
ejpam-2979	144	14	2n	2n	NUM
ejpam-2979	144	15	i	i	NOUN
ejpam-2979	144	16	)	)	PUNCT
ejpam-2979	144	17	(	(	PUNCT
ejpam-2979	144	18	(	(	PUNCT
ejpam-2979	144	19	−q)kc2k	−q)kc2k	VERB
ejpam-2979	144	20	+	+	CCONJ
ejpam-2979	144	21	ckvk	ckvk	NOUN
ejpam-2979	145	1	+	+	CCONJ
ejpam-2979	145	2	1	1	NUM
ejpam-2979	146	1	)	)	PUNCT
ejpam-2979	146	2	i	i	PRON
ejpam-2979	146	3	a−2i	a−2i	PUNCT
ejpam-2979	146	4	=	=	PUNCT
ejpam-2979	146	5	(	(	PUNCT
ejpam-2979	146	6	ckvk	ckvk	VERB
ejpam-2979	146	7	+	+	CCONJ
ejpam-2979	146	8	2	2	NUM
ejpam-2979	146	9	)	)	PUNCT
ejpam-2979	146	10	2n	2n	NUM
ejpam-2979	146	11	a−2n	a−2n	PROPN
ejpam-2979	147	1	2n∑	2n∑	PROPN
ejpam-2979	147	2	i=0	i=0	PROPN
ejpam-2979	147	3	(	(	PUNCT
ejpam-2979	147	4	2n	2n	NUM
ejpam-2979	147	5	i	i	NOUN
ejpam-2979	147	6	)	)	PUNCT
ejpam-2979	147	7	(	(	PUNCT
ejpam-2979	147	8	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	147	9	+	+	CCONJ
ejpam-2979	147	10	ckvk	ckvk	NOUN
ejpam-2979	147	11	+	+	CCONJ
ejpam-2979	147	12	1	1	NUM
ejpam-2979	147	13	)	)	PUNCT
ejpam-2979	147	14	i	i	PRON
ejpam-2979	147	15	[	[	PUNCT
ejpam-2979	147	16	gk(−2i+1	gk(−2i+1	NOUN
ejpam-2979	147	17	)	)	PUNCT
ejpam-2979	147	18	g−2ki	g−2ki	NOUN
ejpam-2979	147	19	]	]	PUNCT
ejpam-2979	148	1	=	=	PUNCT
ejpam-2979	148	2	(	(	PUNCT
ejpam-2979	148	3	ckvk	ckvk	VERB
ejpam-2979	148	4	+	+	CCONJ
ejpam-2979	148	5	2	2	NUM
ejpam-2979	148	6	)	)	PUNCT
ejpam-2979	148	7	2n	2n	NUM
ejpam-2979	148	8	[	[	PUNCT
ejpam-2979	148	9	gk(−2n+1	gk(−2n+1	NOUN
ejpam-2979	148	10	)	)	PUNCT
ejpam-2979	148	11	g−2kn	g−2kn	NOUN
ejpam-2979	148	12	]	]	PUNCT
ejpam-2979	148	13	.	.	PUNCT
ejpam-2979	149	1	thus	thus	ADV
ejpam-2979	149	2	,	,	PUNCT
ejpam-2979	149	3	the	the	DET
ejpam-2979	149	4	proof	proof	NOUN
ejpam-2979	149	5	is	be	AUX
ejpam-2979	149	6	completed	complete	VERB
ejpam-2979	149	7	.	.	PUNCT
ejpam-2979	150	1	let	let	VERB
ejpam-2979	150	2	c	c	PRON
ejpam-2979	150	3	be	be	AUX
ejpam-2979	150	4	an	an	DET
ejpam-2979	150	5	arbitrary	arbitrary	ADJ
ejpam-2979	150	6	2×	2×	NUM
ejpam-2979	150	7	2	2	NUM
ejpam-2979	150	8	matrix	matrix	NOUN
ejpam-2979	150	9	,	,	PUNCT
ejpam-2979	150	10	t	t	PROPN
ejpam-2979	150	11	and	and	CCONJ
ejpam-2979	150	12	d	d	PROPN
ejpam-2979	150	13	denote	denote	VERB
ejpam-2979	150	14	the	the	DET
ejpam-2979	150	15	trace	trace	NOUN
ejpam-2979	150	16	and	and	CCONJ
ejpam-2979	150	17	determinant	determinant	ADJ
ejpam-2979	150	18	of	of	ADP
ejpam-2979	150	19	c	c	NOUN
ejpam-2979	150	20	,	,	PUNCT
ejpam-2979	150	21	respectively	respectively	ADV
ejpam-2979	150	22	.	.	PUNCT
ejpam-2979	151	1	for	for	ADP
ejpam-2979	151	2	the	the	DET
ejpam-2979	151	3	distinct	distinct	NOUN
ejpam-2979	151	4	eigenvalues	eigenvalue	VERB
ejpam-2979	151	5	a	a	PRON
ejpam-2979	151	6	and	and	CCONJ
ejpam-2979	151	7	b	b	NOUN
ejpam-2979	151	8	of	of	ADP
ejpam-2979	151	9	matrix	matrix	NOUN
ejpam-2979	151	10	c	c	NOUN
ejpam-2979	151	11	,	,	PUNCT
ejpam-2979	151	12	the	the	DET
ejpam-2979	151	13	following	following	ADJ
ejpam-2979	151	14	result	result	NOUN
ejpam-2979	151	15	can	can	AUX
ejpam-2979	151	16	be	be	AUX
ejpam-2979	151	17	found	find	VERB
ejpam-2979	151	18	in	in	ADP
ejpam-2979	151	19	[	[	X
ejpam-2979	151	20	5	5	NUM
ejpam-2979	151	21	,	,	PUNCT
ejpam-2979	151	22	10	10	NUM
ejpam-2979	151	23	]	]	PUNCT
ejpam-2979	151	24	:	:	PUNCT
ejpam-2979	151	25	lemma	lemma	PROPN
ejpam-2979	151	26	5	5	NUM
ejpam-2979	151	27	.	.	PUNCT
ejpam-2979	151	28	zn	zn	PROPN
ejpam-2979	151	29	:	:	PUNCT
ejpam-2979	152	1	=	=	PUNCT
ejpam-2979	152	2	an	an	DET
ejpam-2979	152	3	−	−	PROPN
ejpam-2979	152	4	bn	bn	NOUN
ejpam-2979	152	5	a−	a−	PROPN
ejpam-2979	152	6	b	b	NOUN
ejpam-2979	152	7	=	=	SYM
ejpam-2979	152	8	1	1	NUM
ejpam-2979	152	9	2n−1	2n−1	NUM
ejpam-2979	152	10	b(n−1)/2c∑	b(n−1)/2c∑	X
ejpam-2979	152	11	i=0	i=0	PROPN
ejpam-2979	152	12	(	(	PUNCT
ejpam-2979	152	13	n	n	ADV
ejpam-2979	152	14	2i+	2i+	NUM
ejpam-2979	152	15	1	1	NUM
ejpam-2979	152	16	)	)	PUNCT
ejpam-2979	152	17	tn−2i−1(t	tn−2i−1(t	NOUN
ejpam-2979	152	18	2	2	NUM
ejpam-2979	152	19	−	−	NOUN
ejpam-2979	152	20	4d)i	4d)i	NUM
ejpam-2979	152	21	,	,	PUNCT
ejpam-2979	152	22	then	then	ADV
ejpam-2979	152	23	cn	cn	PROPN
ejpam-2979	152	24	=	=	PROPN
ejpam-2979	152	25	znc	znc	PROPN
ejpam-2979	152	26	−	−	PROPN
ejpam-2979	152	27	zn−1di2	zn−1di2	PROPN
ejpam-2979	152	28	,	,	PUNCT
ejpam-2979	152	29	where	where	SCONJ
ejpam-2979	152	30	i2	i2	PROPN
ejpam-2979	152	31	is	be	AUX
ejpam-2979	152	32	the	the	DET
ejpam-2979	152	33	identity	identity	NOUN
ejpam-2979	152	34	matrix	matrix	NOUN
ejpam-2979	152	35	of	of	ADP
ejpam-2979	152	36	order	order	NOUN
ejpam-2979	152	37	2	2	X
ejpam-2979	152	38	.	.	PUNCT
ejpam-2979	153	1	as	as	ADP
ejpam-2979	153	2	a	a	DET
ejpam-2979	153	3	consequence	consequence	NOUN
ejpam-2979	153	4	of	of	ADP
ejpam-2979	153	5	lemma	lemma	PROPN
ejpam-2979	153	6	5	5	NUM
ejpam-2979	153	7	,	,	PUNCT
ejpam-2979	153	8	we	we	PRON
ejpam-2979	153	9	obtain	obtain	VERB
ejpam-2979	153	10	that	that	PRON
ejpam-2979	153	11	2n−1gkn	2n−1gkn	NOUN
ejpam-2979	154	1	=	=	SYM
ejpam-2979	154	2	ukc	ukc	NOUN
ejpam-2979	154	3	k	k	PROPN
ejpam-2979	154	4	b(n−1)/2c∑	b(n−1)/2c∑	PROPN
ejpam-2979	154	5	i=0	i=0	PROPN
ejpam-2979	154	6	(	(	PUNCT
ejpam-2979	154	7	n	n	ADV
ejpam-2979	154	8	2i+	2i+	NUM
ejpam-2979	154	9	1	1	NUM
ejpam-2979	154	10	)	)	PUNCT
ejpam-2979	154	11	(	(	PUNCT
ejpam-2979	154	12	ckvk	ckvk	VERB
ejpam-2979	154	13	+	+	CCONJ
ejpam-2979	154	14	2	2	NUM
ejpam-2979	154	15	)	)	PUNCT
ejpam-2979	154	16	n−2i−1	n−2i−1	NOUN
ejpam-2979	154	17	(	(	PUNCT
ejpam-2979	154	18	c2kv2k	c2kv2k	X
ejpam-2979	154	19	−	−	X
ejpam-2979	155	1	4c2k	4c2k	INTJ
ejpam-2979	156	1	(	(	PUNCT
ejpam-2979	156	2	−q)k)i	−q)k)i	PROPN
ejpam-2979	156	3	.	.	PUNCT
ejpam-2979	157	1	references	reference	NOUN
ejpam-2979	157	2	514	514	NUM
ejpam-2979	157	3	let	let	VERB
ejpam-2979	157	4	w	w	NOUN
ejpam-2979	157	5	be	be	AUX
ejpam-2979	157	6	a	a	DET
ejpam-2979	157	7	complex	complex	ADJ
ejpam-2979	157	8	number	number	NOUN
ejpam-2979	157	9	such	such	ADJ
ejpam-2979	157	10	that	that	DET
ejpam-2979	157	11	w2	w2	NOUN
ejpam-2979	157	12	+	+	CCONJ
ejpam-2979	157	13	tw	tw	NOUN
ejpam-2979	158	1	+	+	ADJ
ejpam-2979	158	2	d	d	NOUN
ejpam-2979	158	3	6=	6=	ADP
ejpam-2979	158	4	0	0	NUM
ejpam-2979	158	5	,	,	PUNCT
ejpam-2979	158	6	w	w	ADP
ejpam-2979	158	7	6=	6=	PROPN
ejpam-2979	158	8	0	0	NUM
ejpam-2979	158	9	.	.	PUNCT
ejpam-2979	159	1	for	for	ADP
ejpam-2979	159	2	a	a	DET
ejpam-2979	159	3	positive	positive	ADJ
ejpam-2979	159	4	integer	integer	NOUN
ejpam-2979	159	5	n	n	NOUN
ejpam-2979	159	6	,	,	PUNCT
ejpam-2979	159	7	cn	cn	X
ejpam-2979	159	8	=	=	SYM
ejpam-2979	159	9	(	(	PUNCT
ejpam-2979	159	10	wd	wd	PROPN
ejpam-2979	159	11	w2	w2	PROPN
ejpam-2979	159	12	+	+	CCONJ
ejpam-2979	159	13	tw	tw	NOUN
ejpam-2979	160	1	+	+	ADJ
ejpam-2979	160	2	d	d	NOUN
ejpam-2979	160	3	)	)	PUNCT
ejpam-2979	160	4	n	n	PROPN
ejpam-2979	160	5	2n∑	2n∑	NUM
ejpam-2979	160	6	t=0	t=0	ADJ
ejpam-2979	160	7	t∑	t∑	PROPN
ejpam-2979	160	8	i=0	i=0	PROPN
ejpam-2979	160	9	(	(	PUNCT
ejpam-2979	160	10	n	n	NOUN
ejpam-2979	160	11	i	i	NOUN
ejpam-2979	160	12	)	)	PUNCT
ejpam-2979	160	13	(	(	PUNCT
ejpam-2979	160	14	n	n	CCONJ
ejpam-2979	160	15	t−	t−	PROPN
ejpam-2979	160	16	i	i	NOUN
ejpam-2979	160	17	)	)	PUNCT
ejpam-2979	160	18	(	(	PUNCT
ejpam-2979	160	19	d	d	PROPN
ejpam-2979	160	20	w2	w2	PROPN
ejpam-2979	160	21	)	)	PUNCT
ejpam-2979	161	1	i	i	PROPN
ejpam-2979	161	2	(	(	PUNCT
ejpam-2979	161	3	w	w	PROPN
ejpam-2979	161	4	d	d	PROPN
ejpam-2979	161	5	)	)	PUNCT
ejpam-2979	161	6	t	t	PROPN
ejpam-2979	161	7	ct	ct	PROPN
ejpam-2979	161	8	.	.	PUNCT
ejpam-2979	162	1	(	(	PUNCT
ejpam-2979	162	2	11	11	NUM
ejpam-2979	162	3	)	)	PUNCT
ejpam-2979	162	4	therefore	therefore	ADV
ejpam-2979	162	5	we	we	PRON
ejpam-2979	162	6	get	get	VERB
ejpam-2979	162	7	the	the	DET
ejpam-2979	162	8	following	following	ADJ
ejpam-2979	162	9	result	result	NOUN
ejpam-2979	162	10	of	of	ADP
ejpam-2979	162	11	equality	equality	NOUN
ejpam-2979	162	12	(	(	PUNCT
ejpam-2979	162	13	11	11	NUM
ejpam-2979	162	14	)	)	PUNCT
ejpam-2979	162	15	.	.	PUNCT
ejpam-2979	163	1	theorem	theorem	VERB
ejpam-2979	163	2	7	7	NUM
ejpam-2979	163	3	.	.	NOUN
ejpam-2979	163	4	for	for	ADP
ejpam-2979	163	5	n	n	PROPN
ejpam-2979	163	6	>	>	SYM
ejpam-2979	163	7	0	0	PUNCT
ejpam-2979	163	8	and	and	CCONJ
ejpam-2979	163	9	any	any	DET
ejpam-2979	163	10	complex	complex	ADJ
ejpam-2979	163	11	number	number	NOUN
ejpam-2979	163	12	w	w	NOUN
ejpam-2979	163	13	different	different	ADJ
ejpam-2979	163	14	from	from	ADP
ejpam-2979	163	15	0	0	NUM
ejpam-2979	163	16	,	,	PUNCT
ejpam-2979	163	17	ckαk+1	ckαk+1	NOUN
ejpam-2979	163	18	and	and	CCONJ
ejpam-2979	163	19	ckβk+1	ckβk+1	NOUN
ejpam-2979	163	20	,	,	PUNCT
ejpam-2979	163	21	gkn	gkn	NOUN
ejpam-2979	163	22	=	=	SYM
ejpam-2979	163	23			PROPN
ejpam-2979	163	24	w	w	PROPN
ejpam-2979	163	25	(	(	PUNCT
ejpam-2979	163	26	c2k	c2k	X
ejpam-2979	163	27	(	(	PUNCT
ejpam-2979	163	28	−q)k	−q)k	NOUN
ejpam-2979	163	29	+	+	CCONJ
ejpam-2979	163	30	ckvk	ckvk	VERB
ejpam-2979	163	31	+	+	CCONJ
ejpam-2979	163	32	1	1	X
ejpam-2979	163	33	)	)	PUNCT
ejpam-2979	163	34	w2	w2	NOUN
ejpam-2979	163	35	+	+	CCONJ
ejpam-2979	163	36	(	(	PUNCT
ejpam-2979	163	37	ckvk	ckvk	VERB
ejpam-2979	163	38	+	+	CCONJ
ejpam-2979	163	39	2)w	2)w	NUM
ejpam-2979	163	40	+	+	CCONJ
ejpam-2979	163	41	(	(	PUNCT
ejpam-2979	163	42	c2k(−q)k	c2k(−q)k	NOUN
ejpam-2979	163	43	+	+	CCONJ
ejpam-2979	163	44	ckvk	ckvk	NOUN
ejpam-2979	163	45	+	+	CCONJ
ejpam-2979	163	46	1	1	NUM
ejpam-2979	163	47	)	)	PUNCT
ejpam-2979	163	48	n	n	PUNCT
ejpam-2979	163	49	×	×	PROPN
ejpam-2979	163	50	2n∑	2n∑	NUM
ejpam-2979	163	51	t=0	t=0	PUNCT
ejpam-2979	163	52	t∑	t∑	PROPN
ejpam-2979	163	53	i=0	i=0	PROPN
ejpam-2979	163	54	(	(	PUNCT
ejpam-2979	163	55	n	n	NOUN
ejpam-2979	163	56	i	i	NOUN
ejpam-2979	163	57	)	)	PUNCT
ejpam-2979	163	58	(	(	PUNCT
ejpam-2979	163	59	n	n	CCONJ
ejpam-2979	163	60	t−	t−	PROPN
ejpam-2979	163	61	i	i	PRON
ejpam-2979	163	62	)	)	PUNCT
ejpam-2979	163	63	(	(	PUNCT
ejpam-2979	163	64	qk(−1)kc2k	qk(−1)kc2k	ADV
ejpam-2979	163	65	+	+	CCONJ
ejpam-2979	163	66	ckvk	ckvk	VERB
ejpam-2979	163	67	+	+	CCONJ
ejpam-2979	163	68	1	1	NUM
ejpam-2979	163	69	)	)	PUNCT
ejpam-2979	163	70	i−t	i−t	PROPN
ejpam-2979	163	71	wt−2igkt	wt−2igkt	PROPN
ejpam-2979	163	72	.	.	PUNCT
ejpam-2979	164	1	references	reference	NOUN
ejpam-2979	164	2	[	[	X
ejpam-2979	164	3	1	1	NUM
ejpam-2979	164	4	]	]	PUNCT
ejpam-2979	164	5	h.	h.	PROPN
ejpam-2979	164	6	belbachir	belbachir	PROPN
ejpam-2979	164	7	,	,	PUNCT
ejpam-2979	164	8	t.	t.	PROPN
ejpam-2979	164	9	komatsu	komatsu	PROPN
ejpam-2979	164	10	and	and	CCONJ
ejpam-2979	164	11	l.	l.	PROPN
ejpam-2979	164	12	szalay	szalay	NOUN
ejpam-2979	164	13	,	,	PUNCT
ejpam-2979	164	14	characterization	characterization	NOUN
ejpam-2979	164	15	of	of	ADP
ejpam-2979	164	16	linear	linear	ADJ
ejpam-2979	164	17	recurrences	recurrence	NOUN
ejpam-2979	164	18	associated	associate	VERB
ejpam-2979	164	19	to	to	ADP
ejpam-2979	164	20	rays	ray	NOUN
ejpam-2979	164	21	in	in	ADP
ejpam-2979	164	22	pascal	pascal	PROPN
ejpam-2979	164	23	’s	’s	PART
ejpam-2979	164	24	triangle	triangle	NOUN
ejpam-2979	164	25	,	,	PUNCT
ejpam-2979	164	26	aip	aip	PROPN
ejpam-2979	164	27	conf	conf	PROPN
ejpam-2979	164	28	.	.	PUNCT
ejpam-2979	165	1	proc	proc	PROPN
ejpam-2979	165	2	.	.	PUNCT
ejpam-2979	166	1	1264	1264	NUM
ejpam-2979	166	2	(	(	PUNCT
ejpam-2979	166	3	2010	2010	NUM
ejpam-2979	166	4	)	)	PUNCT
ejpam-2979	167	1	,	,	PUNCT
ejpam-2979	167	2	90	90	NUM
ejpam-2979	167	3	-	-	SYM
ejpam-2979	167	4	99	99	NUM
ejpam-2979	167	5	;	;	PUNCT
ejpam-2979	167	6	diophantine	diophantine	VERB
ejpam-2979	167	7	analysis	analysis	NOUN
ejpam-2979	167	8	and	and	CCONJ
ejpam-2979	167	9	related	relate	VERB
ejpam-2979	167	10	fields	field	NOUN
ejpam-2979	167	11	2000	2000	NUM
ejpam-2979	167	12	,	,	PUNCT
ejpam-2979	167	13	amer	amer	PROPN
ejpam-2979	167	14	.	.	PROPN
ejpam-2979	167	15	math	math	PROPN
ejpam-2979	167	16	.	.	PUNCT
ejpam-2979	168	1	phys	phy	NOUN
ejpam-2979	168	2	.	.	PUNCT
ejpam-2979	168	3	,	,	PUNCT
ejpam-2979	168	4	melville	melville	PROPN
ejpam-2979	168	5	,	,	PUNCT
ejpam-2979	168	6	ny	ny	PROPN
ejpam-2979	168	7	,	,	PUNCT
ejpam-2979	168	8	2010	2010	NUM
ejpam-2979	168	9	.	.	PUNCT
ejpam-2979	169	1	[	[	X
ejpam-2979	169	2	2	2	NUM
ejpam-2979	169	3	]	]	PUNCT
ejpam-2979	169	4	h.	h.	PROPN
ejpam-2979	169	5	belbachir	belbachir	PROPN
ejpam-2979	169	6	,	,	PUNCT
ejpam-2979	169	7	t.	t.	PROPN
ejpam-2979	169	8	komatsu	komatsu	PROPN
ejpam-2979	169	9	and	and	CCONJ
ejpam-2979	169	10	l.	l.	PROPN
ejpam-2979	169	11	szalay	szalay	PROPN
ejpam-2979	169	12	,	,	PUNCT
ejpam-2979	169	13	linear	linear	ADJ
ejpam-2979	169	14	recurrences	recurrence	NOUN
ejpam-2979	169	15	associated	associate	VERB
ejpam-2979	169	16	to	to	ADP
ejpam-2979	169	17	rays	ray	NOUN
ejpam-2979	169	18	in	in	ADP
ejpam-2979	169	19	pascal	pascal	PROPN
ejpam-2979	169	20	’s	’s	PART
ejpam-2979	169	21	triangle	triangle	NOUN
ejpam-2979	169	22	and	and	CCONJ
ejpam-2979	169	23	combinatorial	combinatorial	ADJ
ejpam-2979	169	24	identities	identity	NOUN
ejpam-2979	169	25	,	,	PUNCT
ejpam-2979	169	26	math	math	NOUN
ejpam-2979	169	27	.	.	PUNCT
ejpam-2979	170	1	slovaca	slovaca	PROPN
ejpam-2979	170	2	,	,	PUNCT
ejpam-2979	170	3	64(2	64(2	NUM
ejpam-2979	170	4	)	)	PUNCT
ejpam-2979	170	5	(	(	PUNCT
ejpam-2979	170	6	2014	2014	NUM
ejpam-2979	170	7	)	)	PUNCT
ejpam-2979	170	8	,	,	PUNCT
ejpam-2979	170	9	287	287	NUM
ejpam-2979	170	10	-	-	SYM
ejpam-2979	170	11	300	300	NUM
ejpam-2979	170	12	..	..	PUNCT
ejpam-2979	171	1	[	[	X
ejpam-2979	171	2	3	3	NUM
ejpam-2979	171	3	]	]	X
ejpam-2979	171	4	n.h	n.h	PROPN
ejpam-2979	171	5	.	.	PROPN
ejpam-2979	171	6	bong	bong	PROPN
ejpam-2979	171	7	,	,	PUNCT
ejpam-2979	171	8	fibonacci	fibonacci	NOUN
ejpam-2979	171	9	matrices	matrix	NOUN
ejpam-2979	171	10	and	and	CCONJ
ejpam-2979	171	11	matrix	matrix	NOUN
ejpam-2979	171	12	representation	representation	NOUN
ejpam-2979	171	13	of	of	ADP
ejpam-2979	171	14	fibonacci	fibonacci	NOUN
ejpam-2979	171	15	numbers	number	NOUN
ejpam-2979	171	16	,	,	PUNCT
ejpam-2979	171	17	southeast	southeast	ADJ
ejpam-2979	171	18	asian	asian	ADJ
ejpam-2979	171	19	bull	bull	NOUN
ejpam-2979	171	20	.	.	PUNCT
ejpam-2979	172	1	math	math	NOUN
ejpam-2979	172	2	.	.	PUNCT
ejpam-2979	173	1	,	,	PUNCT
ejpam-2979	173	2	23	23	NUM
ejpam-2979	173	3	(	(	PUNCT
ejpam-2979	173	4	1999	1999	NUM
ejpam-2979	173	5	)	)	PUNCT
ejpam-2979	173	6	,	,	PUNCT
ejpam-2979	173	7	357	357	NUM
ejpam-2979	173	8	-	-	SYM
ejpam-2979	173	9	374	374	NUM
ejpam-2979	173	10	.	.	PUNCT
ejpam-2979	174	1	[	[	X
ejpam-2979	174	2	4	4	NUM
ejpam-2979	174	3	]	]	X
ejpam-2979	174	4	c.	c.	PROPN
ejpam-2979	174	5	k.	k.	PROPN
ejpam-2979	174	6	cook	cook	PROPN
ejpam-2979	174	7	and	and	CCONJ
ejpam-2979	174	8	t.	t.	PROPN
ejpam-2979	174	9	komatsu	komatsu	PROPN
ejpam-2979	174	10	,	,	PUNCT
ejpam-2979	174	11	some	some	DET
ejpam-2979	174	12	identities	identity	NOUN
ejpam-2979	174	13	for	for	ADP
ejpam-2979	174	14	sequences	sequence	NOUN
ejpam-2979	174	15	ob	ob	CCONJ
ejpam-2979	174	16	binomial	binomial	ADJ
ejpam-2979	174	17	sums	sum	NOUN
ejpam-2979	174	18	of	of	ADP
ejpam-2979	174	19	generalized	generalized	ADJ
ejpam-2979	174	20	fibonacci	fibonacci	NOUN
ejpam-2979	174	21	numbers	number	NOUN
ejpam-2979	174	22	,	,	PUNCT
ejpam-2979	174	23	the	the	DET
ejpam-2979	174	24	fibonacci	fibonacci	NOUN
ejpam-2979	174	25	quarterly	quarterly	PROPN
ejpam-2979	174	26	,	,	PUNCT
ejpam-2979	174	27	54(2	54(2	NUM
ejpam-2979	174	28	)	)	PUNCT
ejpam-2979	174	29	(	(	PUNCT
ejpam-2979	174	30	2016	2016	NUM
ejpam-2979	174	31	)	)	PUNCT
ejpam-2979	174	32	,	,	PUNCT
ejpam-2979	174	33	105	105	NUM
ejpam-2979	174	34	-	-	SYM
ejpam-2979	174	35	111	111	NUM
ejpam-2979	174	36	.	.	PUNCT
ejpam-2979	175	1	[	[	X
ejpam-2979	175	2	5	5	NUM
ejpam-2979	175	3	]	]	PUNCT
ejpam-2979	175	4	p.	p.	NOUN
ejpam-2979	175	5	haukkanen	haukkanen	PROPN
ejpam-2979	175	6	,	,	PUNCT
ejpam-2979	175	7	binomial	binomial	ADJ
ejpam-2979	175	8	formulas	formula	NOUN
ejpam-2979	175	9	for	for	ADP
ejpam-2979	175	10	specially	specially	ADV
ejpam-2979	175	11	multiplicative	multiplicative	ADJ
ejpam-2979	175	12	functions	function	NOUN
ejpam-2979	175	13	,	,	PUNCT
ejpam-2979	175	14	math	math	NOUN
ejpam-2979	175	15	.	.	PUNCT
ejpam-2979	176	1	student	student	NOUN
ejpam-2979	176	2	64(1	64(1	NUM
ejpam-2979	176	3	-	-	SYM
ejpam-2979	176	4	4	4	NUM
ejpam-2979	176	5	)	)	PUNCT
ejpam-2979	176	6	(	(	PUNCT
ejpam-2979	176	7	1995	1995	NUM
ejpam-2979	176	8	)	)	PUNCT
ejpam-2979	176	9	,	,	PUNCT
ejpam-2979	176	10	155	155	NUM
ejpam-2979	176	11	-	-	SYM
ejpam-2979	176	12	161	161	NUM
ejpam-2979	176	13	.	.	PUNCT
ejpam-2979	177	1	[	[	X
ejpam-2979	177	2	6	6	NUM
ejpam-2979	177	3	]	]	X
ejpam-2979	177	4	v.e	v.e	PROPN
ejpam-2979	177	5	.	.	PROPN
ejpam-2979	177	6	hoggat	hoggat	PROPN
ejpam-2979	177	7	,	,	PUNCT
ejpam-2979	177	8	jr	jr	PROPN
ejpam-2979	177	9	and	and	CCONJ
ejpam-2979	177	10	m.	m.	PROPN
ejpam-2979	177	11	bicknell	bicknell	PROPN
ejpam-2979	177	12	-	-	PUNCT
ejpam-2979	177	13	johnson	johnson	PROPN
ejpam-2979	177	14	,	,	PUNCT
ejpam-2979	177	15	a	a	DET
ejpam-2979	177	16	matrix	matrix	NOUN
ejpam-2979	177	17	representation	representation	NOUN
ejpam-2979	177	18	of	of	ADP
ejpam-2979	177	19	fibonacci	fibonacci	NOUN
ejpam-2979	177	20	identities	identity	NOUN
ejpam-2979	177	21	for	for	ADP
ejpam-2979	177	22	f2nk	f2nk	NOUN
ejpam-2979	177	23	,	,	PUNCT
ejpam-2979	177	24	a	a	DET
ejpam-2979	177	25	collection	collection	NOUN
ejpam-2979	177	26	of	of	ADP
ejpam-2979	177	27	manuscripts	manuscript	NOUN
ejpam-2979	177	28	related	relate	VERB
ejpam-2979	177	29	to	to	ADP
ejpam-2979	177	30	the	the	DET
ejpam-2979	177	31	fibonacci	fibonacci	NOUN
ejpam-2979	177	32	sequence	sequence	NOUN
ejpam-2979	177	33	,	,	PUNCT
ejpam-2979	177	34	18th	18th	ADJ
ejpam-2979	177	35	anniversary	anniversary	NOUN
ejpam-2979	177	36	volume	volume	NOUN
ejpam-2979	177	37	,	,	PUNCT
ejpam-2979	177	38	pp	pp	ADP
ejpam-2979	177	39	.	.	PUNCT
ejpam-2979	178	1	114	114	NUM
ejpam-2979	178	2	-	-	SYM
ejpam-2979	178	3	124	124	NUM
ejpam-2979	178	4	,	,	PUNCT
ejpam-2979	178	5	the	the	DET
ejpam-2979	178	6	fibonacci	fibonacci	PROPN
ejpam-2979	178	7	association	association	PROPN
ejpam-2979	178	8	,	,	PUNCT
ejpam-2979	178	9	1980	1980	NUM
ejpam-2979	178	10	.	.	PUNCT
ejpam-2979	179	1	[	[	X
ejpam-2979	179	2	7	7	X
ejpam-2979	179	3	]	]	X
ejpam-2979	179	4	e.	e.	PROPN
ejpam-2979	179	5	kılıç	kılıç	PROPN
ejpam-2979	179	6	and	and	CCONJ
ejpam-2979	179	7	p.stanica	p.stanica	PROPN
ejpam-2979	179	8	,	,	PUNCT
ejpam-2979	179	9	factorizations	factorization	NOUN
ejpam-2979	179	10	and	and	CCONJ
ejpam-2979	179	11	representations	representation	NOUN
ejpam-2979	179	12	of	of	ADP
ejpam-2979	179	13	second	second	ADJ
ejpam-2979	179	14	order	order	NOUN
ejpam-2979	179	15	linear	linear	NOUN
ejpam-2979	179	16	recurrences	recurrence	NOUN
ejpam-2979	179	17	with	with	ADP
ejpam-2979	179	18	indices	index	NOUN
ejpam-2979	179	19	in	in	ADP
ejpam-2979	179	20	arithmetic	arithmetic	ADJ
ejpam-2979	179	21	progressions	progression	NOUN
ejpam-2979	179	22	,	,	PUNCT
ejpam-2979	179	23	bulletin	bulletin	NOUN
ejpam-2979	179	24	of	of	ADP
ejpam-2979	179	25	the	the	DET
ejpam-2979	179	26	mexican	mexican	PROPN
ejpam-2979	179	27	mathematical	mathematical	ADJ
ejpam-2979	179	28	society	society	NOUN
ejpam-2979	179	29	15(1	15(1	NUM
ejpam-2979	179	30	)	)	PUNCT
ejpam-2979	179	31	(	(	PUNCT
ejpam-2979	179	32	2009	2009	NUM
ejpam-2979	179	33	)	)	PUNCT
ejpam-2979	179	34	,	,	PUNCT
ejpam-2979	179	35	23	23	NUM
ejpam-2979	179	36	-	-	SYM
ejpam-2979	179	37	36	36	NUM
ejpam-2979	179	38	.	.	PUNCT
ejpam-2979	180	1	[	[	X
ejpam-2979	180	2	8	8	NUM
ejpam-2979	180	3	]	]	X
ejpam-2979	180	4	e.	e.	PROPN
ejpam-2979	180	5	kılıç	kılıç	PROPN
ejpam-2979	180	6	,	,	PUNCT
ejpam-2979	180	7	n.	n.	NOUN
ejpam-2979	180	8	ömür	ömür	NOUN
ejpam-2979	180	9	and	and	CCONJ
ejpam-2979	180	10	y.	y.	PROPN
ejpam-2979	180	11	türker	türker	PROPN
ejpam-2979	180	12	ulutaş	ulutaş	PROPN
ejpam-2979	180	13	,	,	PUNCT
ejpam-2979	180	14	matrix	matrix	NOUN
ejpam-2979	180	15	representation	representation	NOUN
ejpam-2979	180	16	of	of	ADP
ejpam-2979	180	17	the	the	DET
ejpam-2979	180	18	second	second	ADJ
ejpam-2979	180	19	order	order	NOUN
ejpam-2979	180	20	recurrence	recurrence	NOUN
ejpam-2979	180	21	{	{	PUNCT
ejpam-2979	180	22	ukn	ukn	NOUN
ejpam-2979	180	23	}	}	PUNCT
ejpam-2979	180	24	,	,	PUNCT
ejpam-2979	180	25	ars	ar	VERB
ejpam-2979	180	26	combinatoria	combinatoria	PROPN
ejpam-2979	180	27	,	,	PUNCT
ejpam-2979	180	28	93	93	NUM
ejpam-2979	180	29	(	(	PUNCT
ejpam-2979	180	30	2009	2009	NUM
ejpam-2979	180	31	)	)	PUNCT
ejpam-2979	180	32	,	,	PUNCT
ejpam-2979	180	33	181	181	NUM
ejpam-2979	180	34	-	-	SYM
ejpam-2979	180	35	190	190	NUM
ejpam-2979	180	36	.	.	PUNCT
ejpam-2979	181	1	[	[	X
ejpam-2979	181	2	9	9	NUM
ejpam-2979	181	3	]	]	X
ejpam-2979	181	4	e.	e.	PROPN
ejpam-2979	181	5	kılıç	kılıç	PROPN
ejpam-2979	181	6	,	,	PUNCT
ejpam-2979	181	7	i.	i.	PROPN
ejpam-2979	181	8	akkuş	akkuş	PROPN
ejpam-2979	181	9	,	,	PUNCT
ejpam-2979	181	10	n.	n.	NOUN
ejpam-2979	181	11	ömür	ömür	NOUN
ejpam-2979	181	12	and	and	CCONJ
ejpam-2979	181	13	y.	y.	PROPN
ejpam-2979	181	14	türker	türker	PROPN
ejpam-2979	181	15	ulutaş	ulutaş	PROPN
ejpam-2979	181	16	,	,	PUNCT
ejpam-2979	181	17	a	a	DET
ejpam-2979	181	18	curious	curious	ADJ
ejpam-2979	181	19	matrix	matrix	NOUN
ejpam-2979	181	20	-	-	PUNCT
ejpam-2979	181	21	sum	sum	NOUN
ejpam-2979	181	22	identity	identity	NOUN
ejpam-2979	181	23	and	and	CCONJ
ejpam-2979	181	24	certain	certain	ADJ
ejpam-2979	181	25	finite	finite	NOUN
ejpam-2979	181	26	sums	sum	NOUN
ejpam-2979	181	27	identities	identity	NOUN
ejpam-2979	181	28	,	,	PUNCT
ejpam-2979	181	29	asian	asian	ADJ
ejpam-2979	181	30	-	-	PUNCT
ejpam-2979	181	31	european	european	ADJ
ejpam-2979	181	32	journal	journal	NOUN
ejpam-2979	181	33	of	of	ADP
ejpam-2979	181	34	mathematics	mathematic	NOUN
ejpam-2979	181	35	,	,	PUNCT
ejpam-2979	181	36	8(3	8(3	NUM
ejpam-2979	181	37	)	)	PUNCT
ejpam-2979	181	38	(	(	PUNCT
ejpam-2979	181	39	2015	2015	NUM
ejpam-2979	181	40	)	)	PUNCT
ejpam-2979	181	41	,	,	PUNCT
ejpam-2979	181	42	1550047	1550047	NUM
ejpam-2979	181	43	-	-	SYM
ejpam-2979	181	44	1	1	NUM
ejpam-2979	181	45	-	-	SYM
ejpam-2979	181	46	10	10	NUM
ejpam-2979	181	47	.	.	PUNCT
ejpam-2979	182	1	references	reference	NOUN
ejpam-2979	182	2	515	515	NUM
ejpam-2979	182	3	[	[	X
ejpam-2979	182	4	10	10	NUM
ejpam-2979	182	5	]	]	PUNCT
ejpam-2979	182	6	j.	j.	PROPN
ejpam-2979	182	7	mc	mc	PROPN
ejpam-2979	182	8	laughlin	laughlin	PROPN
ejpam-2979	182	9	,	,	PUNCT
ejpam-2979	182	10	combinatorial	combinatorial	ADJ
ejpam-2979	182	11	identities	identity	NOUN
ejpam-2979	182	12	deriving	derive	VERB
ejpam-2979	182	13	from	from	ADP
ejpam-2979	182	14	the	the	DET
ejpam-2979	182	15	nth	nth	NOUN
ejpam-2979	182	16	power	power	NOUN
ejpam-2979	182	17	of	of	ADP
ejpam-2979	182	18	a	a	DET
ejpam-2979	182	19	2	2	NUM
ejpam-2979	182	20	×	×	NOUN
ejpam-2979	182	21	2	2	NUM
ejpam-2979	182	22	matrix	matrix	NOUN
ejpam-2979	182	23	,	,	PUNCT
ejpam-2979	182	24	integers	integer	NOUN
ejpam-2979	182	25	,	,	PUNCT
ejpam-2979	182	26	4	4	NUM
ejpam-2979	182	27	(	(	PUNCT
ejpam-2979	182	28	2004	2004	NUM
ejpam-2979	182	29	)	)	PUNCT
ejpam-2979	182	30	a19	a19	PROPN
ejpam-2979	182	31	,	,	PUNCT
ejpam-2979	182	32	15pp	15pp	NOUN
ejpam-2979	182	33	.	.	PUNCT
ejpam-2979	183	1	[	[	X
ejpam-2979	183	2	11	11	NUM
ejpam-2979	183	3	]	]	PUNCT
ejpam-2979	183	4	t.	t.	PROPN
ejpam-2979	183	5	komatsu	komatsu	PROPN
ejpam-2979	183	6	,	,	PUNCT
ejpam-2979	183	7	some	some	DET
ejpam-2979	183	8	generalized	generalized	ADJ
ejpam-2979	183	9	fibonacci	fibonacci	NOUN
ejpam-2979	183	10	identitis	identitis	PROPN
ejpam-2979	183	11	including	include	VERB
ejpam-2979	183	12	powers	power	NOUN
ejpam-2979	183	13	and	and	CCONJ
ejpam-2979	183	14	binomial	binomial	ADJ
ejpam-2979	183	15	coefficients	coefficient	NOUN
ejpam-2979	183	16	,	,	PUNCT
ejpam-2979	183	17	the	the	DET
ejpam-2979	183	18	fibonacci	fibonacci	NOUN
ejpam-2979	183	19	quarterly	quarterly	ADV
ejpam-2979	183	20	,	,	PUNCT
ejpam-2979	183	21	52(1	52(1	NOUN
ejpam-2979	183	22	)	)	PUNCT
ejpam-2979	183	23	(	(	PUNCT
ejpam-2979	183	24	2014	2014	NUM
ejpam-2979	183	25	)	)	PUNCT
ejpam-2979	183	26	,	,	PUNCT
ejpam-2979	183	27	50	50	NUM
ejpam-2979	183	28	-	-	SYM
ejpam-2979	183	29	60	60	NUM
ejpam-2979	183	30	.	.	PUNCT
ejpam-2979	184	1	[	[	X
ejpam-2979	184	2	12	12	NUM
ejpam-2979	184	3	]	]	X
ejpam-2979	184	4	t.	t.	PROPN
ejpam-2979	184	5	koshy	koshy	PROPN
ejpam-2979	184	6	,	,	PUNCT
ejpam-2979	184	7	fibonacci	fibonacci	NOUN
ejpam-2979	184	8	and	and	CCONJ
ejpam-2979	184	9	lucas	lucas	PROPN
ejpam-2979	184	10	numbers	number	NOUN
ejpam-2979	184	11	with	with	ADP
ejpam-2979	184	12	applications	application	NOUN
ejpam-2979	184	13	,	,	PUNCT
ejpam-2979	184	14	a	a	DET
ejpam-2979	184	15	wiley	wiley	NOUN
ejpam-2979	184	16	-	-	PUNCT
ejpam-2979	184	17	interscience	interscience	NOUN
ejpam-2979	184	18	publications	publication	NOUN
ejpam-2979	184	19	,	,	PUNCT
ejpam-2979	184	20	new	new	PROPN
ejpam-2979	184	21	york	york	PROPN
ejpam-2979	184	22	,	,	PUNCT
ejpam-2979	184	23	2001	2001	NUM
ejpam-2979	184	24	.	.	PUNCT
ejpam-2979	185	1	[	[	X
ejpam-2979	185	2	13	13	NUM
ejpam-2979	185	3	]	]	PUNCT
ejpam-2979	185	4	j.	j.	PROPN
ejpam-2979	185	5	mc	mc	PROPN
ejpam-2979	185	6	laughlin	laughlin	PROPN
ejpam-2979	185	7	,	,	PUNCT
ejpam-2979	185	8	combinatorial	combinatorial	ADJ
ejpam-2979	185	9	identities	identity	NOUN
ejpam-2979	185	10	deriving	derive	VERB
ejpam-2979	185	11	from	from	ADP
ejpam-2979	185	12	the	the	DET
ejpam-2979	185	13	nth	nth	NOUN
ejpam-2979	185	14	power	power	NOUN
ejpam-2979	185	15	of	of	ADP
ejpam-2979	185	16	a	a	DET
ejpam-2979	185	17	2	2	NUM
ejpam-2979	185	18	×	×	NOUN
ejpam-2979	185	19	2	2	NUM
ejpam-2979	185	20	matrix	matrix	NOUN
ejpam-2979	185	21	,	,	PUNCT
ejpam-2979	185	22	integers	integer	NOUN
ejpam-2979	185	23	,	,	PUNCT
ejpam-2979	185	24	4	4	NUM
ejpam-2979	185	25	(	(	PUNCT
ejpam-2979	185	26	2004	2004	NUM
ejpam-2979	185	27	)	)	PUNCT
ejpam-2979	185	28	a19	a19	PROPN
ejpam-2979	185	29	,	,	PUNCT
ejpam-2979	185	30	15pp	15pp	NOUN
ejpam-2979	185	31	.	.	PUNCT
ejpam-2979	186	1	[	[	X
ejpam-2979	186	2	14	14	NUM
ejpam-2979	186	3	]	]	X
ejpam-2979	186	4	j.	j.	PROPN
ejpam-2979	186	5	mc	mc	PROPN
ejpam-2979	186	6	laughlin	laughlin	PROPN
ejpam-2979	186	7	and	and	CCONJ
ejpam-2979	186	8	n.	n.	PROPN
ejpam-2979	186	9	j.	j.	PROPN
ejpam-2979	186	10	wyshinski	wyshinski	PROPN
ejpam-2979	186	11	,	,	PUNCT
ejpam-2979	186	12	further	further	ADJ
ejpam-2979	186	13	combinatorial	combinatorial	ADJ
ejpam-2979	186	14	identities	identity	NOUN
ejpam-2979	186	15	deriving	derive	VERB
ejpam-2979	186	16	from	from	ADP
ejpam-2979	186	17	the	the	DET
ejpam-2979	186	18	nth	nth	NOUN
ejpam-2979	186	19	power	power	NOUN
ejpam-2979	186	20	of	of	ADP
ejpam-2979	186	21	a	a	DET
ejpam-2979	186	22	2×	2×	NUM
ejpam-2979	186	23	2	2	NUM
ejpam-2979	186	24	matrix	matrix	NOUN
ejpam-2979	186	25	,	,	PUNCT
ejpam-2979	186	26	discrete	discrete	ADJ
ejpam-2979	186	27	applied	apply	VERB
ejpam-2979	186	28	mathematics	mathematic	NOUN
ejpam-2979	186	29	,	,	PUNCT
ejpam-2979	186	30	154(8	154(8	NUM
ejpam-2979	186	31	)	)	PUNCT
ejpam-2979	186	32	(	(	PUNCT
ejpam-2979	186	33	2006	2006	NUM
ejpam-2979	186	34	)	)	PUNCT
ejpam-2979	186	35	,	,	PUNCT
ejpam-2979	186	36	13011308	13011308	NUM
ejpam-2979	186	37	.	.	PUNCT
ejpam-2979	187	1	[	[	X
ejpam-2979	187	2	15	15	NUM
ejpam-2979	187	3	]	]	X
ejpam-2979	187	4	m.e	m.e	PROPN
ejpam-2979	187	5	.	.	PROPN
ejpam-2979	187	6	waddill	waddill	PROPN
ejpam-2979	187	7	,	,	PUNCT
ejpam-2979	187	8	matrices	matrix	NOUN
ejpam-2979	187	9	and	and	CCONJ
ejpam-2979	187	10	generalized	generalized	ADJ
ejpam-2979	187	11	fibonacci	fibonacci	NOUN
ejpam-2979	187	12	sequences	sequence	NOUN
ejpam-2979	187	13	,	,	PUNCT
ejpam-2979	187	14	fibonacci	fibonacci	PROPN
ejpam-2979	187	15	quart.12	quart.12	PROPN
ejpam-2979	187	16	(	(	PUNCT
ejpam-2979	187	17	1974	1974	NUM
ejpam-2979	187	18	)	)	PUNCT
ejpam-2979	187	19	,	,	PUNCT
ejpam-2979	187	20	381	381	NUM
ejpam-2979	187	21	-	-	SYM
ejpam-2979	187	22	386	386	NUM
ejpam-2979	187	23	.	.	PUNCT
ejpam-2979	188	1	[	[	X
ejpam-2979	188	2	16	16	NUM
ejpam-2979	188	3	]	]	X
ejpam-2979	188	4	k.s	k.s	PROPN
ejpam-2979	188	5	.	.	PROPN
ejpam-2979	188	6	williams	williams	PROPN
ejpam-2979	188	7	,	,	PUNCT
ejpam-2979	188	8	the	the	DET
ejpam-2979	188	9	nth	nth	NOUN
ejpam-2979	188	10	power	power	NOUN
ejpam-2979	188	11	of	of	ADP
ejpam-2979	188	12	a	a	DET
ejpam-2979	188	13	2×	2×	NUM
ejpam-2979	188	14	2	2	NUM
ejpam-2979	188	15	matrix	matrix	NOUN
ejpam-2979	188	16	,	,	PUNCT
ejpam-2979	188	17	math	math	NOUN
ejpam-2979	188	18	.	.	PUNCT
ejpam-2979	189	1	mag	mag	PROPN
ejpam-2979	189	2	.	.	PUNCT
ejpam-2979	190	1	65(5	65(5	NUM
ejpam-2979	190	2	)	)	PUNCT
ejpam-2979	190	3	(	(	PUNCT
ejpam-2979	190	4	1992	1992	NUM
ejpam-2979	190	5	)	)	PUNCT
ejpam-2979	190	6	,	,	PUNCT
ejpam-2979	190	7	336	336	NUM
ejpam-2979	190	8	.	.	PUNCT