Characterizations and Identities for Isosceles Triangular Numbers

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i2.3952

Keywords:

Integer Sequences, Triangular numbers, Isosceles triangular numbers, Polygonal Numbers, Identities

Abstract

Triangular numbers have been of interest and continuously studied due to their beautiful representations, nice properties, and various links with other figurate numbers. For positive integers n and l, the nth l-isosceles triangular number is a generalization of triangular numbers defined to be the arithmetic sum of the form

T(n, l) = 1 + (1 + l) + (1 + 2l) + · · · + (1 + (n − 1)l).

In this paper, we focus on characterizations and identities for isosceles triangular numbers as well as their links with other figurate numbers. Recursive formulas for constructions of isosceles triangular numbers are given together with necessary and sufficient conditions for a positive integer to be a sum of isosceles triangular  numbers. Various identities for isosceles triangular numbers are established. Results on triangular numbers can be viewed as a special case.

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Published

2021-05-18

Issue

Section

Nonlinear Analysis

How to Cite

Characterizations and Identities for Isosceles Triangular Numbers. (2021). European Journal of Pure and Applied Mathematics, 14(2), 380-395. https://doi.org/10.29020/nybg.ejpam.v14i2.3952