Journal of innovative applied mathematics and computational sciences
Volume 1, Numéro 1, Pages 16-30
2021-12-30

A Study On The Sum Of The Squares Of Generalized Balancing Numbers: The Sum Formula $\sum_{k=0}^{n}x^{k}w_{mk+j}^{2}$



Authors : Soykan Yüksel . Taşdemir Erkan . Dikmen Can Murat .

Abstract

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$ for generalized balancing numbers are presented. As special cases, we give sum formulas of balancing, modified Lucas-balancing and Lucas-balancing numbers.

Keywords

Balancing numbers modified Lucas-balancing numbers Lucas-balancing numbers sum formulas

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