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
Erkan Taşdemir
Can Murat Dikmen


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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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.
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