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

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

• hexanacci numbers
• hexanacci-lucas numbers
• sum formulas
• summing formulas