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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