Characterizations and Identities for Isosceles Triangular Numbers
DOI:
https://doi.org/10.29020/nybg.ejpam.v14i2.3952Keywords:
Integer Sequences, Triangular numbers, Isosceles triangular numbers, Polygonal Numbers, IdentitiesAbstract
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.
Downloads
Published
Issue
Section
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.