A note on sum formulas $\sum_{k=0}^{n}kx^{k}W_{k}$ and $\sum_{k=1}^{n}kx^{k}W_{-k}$ of generalized Hexanacci numbers

Document Type : Research Paper

Authors

1 Department of Mathematics, Art and Science Faculty, Zonguldak Bulent Ecevit University, Zonguldak, Turkey

2 Pinarhisar Vocational School, Kirklareli University, Kirklareli, Turkey

3 Ministry of National Education, Pinarhisar Anatolian High School, Kirklareli, Turkey

Abstract

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

Keywords

References

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  • Receive Date: 01 June 2022
  • Revise Date: 18 August 2022
  • Accept Date: 30 August 2022

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