# 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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## 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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## Article Details

*Journal of Innovative Applied Mathematics and Computational Sciences*. 1, 1 (Dec. 2021), 16–30. DOI:https://doi.org/10.58205/jiamcs.v1i1.7.

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