A study on the sum of the squares of generalized Balancing numbers: the sum formula $\sum_{k=0}^{n}x^{k}W

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

Published:2021-12-27 Issue:1 Volume:1 Page:16-30
ISSN:2773-4196
Container-title:Journal of Innovative Applied Mathematics and Computational Sciences
language:
Short-container-title:J. Innov. Appl. Math. Comput. Sci

Author:

Soykan Yüksel^ORCID,Taşdemir Erkan^ORCID,Dikmen Can Murat^ORCID

Abstract

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

Publisher

Abdelhafid Boussouf university center of Mila

Reference29 articles.

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4. R.K. Davala and G.K. Panda, On Sum and Ratio Formulas for Balancing Numbers, J. Indian Math. Soc. (N.S.) 82(1-2) (2015), 23–32.

5. A.F. Horadam, A Generalized Fibonacci Sequence, Amer. Math. Monthly 68 (1961), 455–459.

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