A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$

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Yüksel Soykan
https://orcid.org/0000-0002-1895-211X
Erkan Taşdemir
https://orcid.org/0000-0002-5002-3193
Can Murat Dikmen
https://orcid.org/0000-0002-1837-1139

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.

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How to Cite
[1]
Soykan, Y., Taşdemir, E. and Dikmen, C.M. 2021. A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W_{mk+j}^{2}$. Journal of Innovative Applied Mathematics and Computational Sciences. 1, 1 (Dec. 2021), 16–30. DOI:https://doi.org/10.58205/jiamcs.v1i1.7.
Section
Research Articles

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