Asian Research Journal of Mathematics

A Study on Sum Formulas of Generalized Hexanacci Numbers: Closed Forms of the Sum Formulas ∑n k=0 xkWk and ∑nk=1 xkW−k

Yüksel Soykan *

Department of Mathematics, Art and Science Faculty, Zonguldak B¨ulent Ecevit University, 67100, Zonguldak, Turkey.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, closed forms of the sum formulas ∑ⁿ _k =0 x^kW_k and ∑ⁿ _k=1 x^kW_-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

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