id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4498	Kobayashi, Yukio	Using the Sum of Triangular Numbers as the most Fundamental Number of Combinations Found using Heuristic Methods	2022	17	.pdf	application/pdf	5090	297	72	Triangular numbers The relationship between the sum of natural numbers and triangular numbers ex- pressed by (17) and (18), respectively, indicates the number of combinations, n+2C3. Square numbers The sum of natural numbers and of triangular numbers can be explained in terms of combinatorics; thus, (20) suggests that the sum of square numbers can also be implied by combinatorics, and a diagram corresponding to Figure 1 can be drawn as shown in Figure 7.	cache/ejpam-4498.pdf	txt/ejpam-4498.txt