A Study on Sum Formulas of Generalized Pentanacci Sequence: Closed Forms of the Sum Formulas ∑_{k=0}ⁿx^{k}W_{k} and ∑_{k=1}ⁿx^{k}W_{-k}

  • Yüksel Soykan Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, 67100, Zonguldak, Turkey
Keywords: Pentanacci numbers, Pentanacci-Lucas numbers, sum formulas, summing formulas.

Abstract

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}$ and $\sum_{k=1}^{n}x^{k}W_{-k}$ for generalized Pentanacci numbers are presented. As special cases, we give summation formulas of Pentanacci, Pentanacci-Lucas, and other fifth-order recurrence sequences.

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Published
2021-05-31
How to Cite
Soykan, Y. (2021). A Study on Sum Formulas of Generalized Pentanacci Sequence: Closed Forms of the Sum Formulas ∑_{k=0}ⁿx^{k}W_{k} and ∑_{k=1}ⁿx^{k}W_{-k}. Journal of Progressive Research in Mathematics, 18(2), 20-38. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2050
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Articles