Triple sums including Fibonacci numbers with three binomial coefficients

Funda Taşdemir
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 188–197
DOI: 10.7546/nntdm.2021.27.1.188-197
Full paper (PDF, 179 Kb)

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Authors and affiliations

Funda Taşdemir
Department of Mathematics, Yozgat Bozok University
Yozgat, Turkey

Abstract

In this paper, we consider some triple sums that involve Fibonacci numbers with three binomial coefficients. We chose the indices of Fibonacci numbers as linear combination of the summation indices. Moreover, various types of alternating analogues of them whose powers depend on the index or indices are computed. These sums are evaluated in nice multiplication forms in terms of Fibonacci and Lucas numbers.

Keywords

• Fibonacci numbers
• Lucas numbers
• Binomial triple sums

2010 Mathematics Subject Classification

• 11B39
• 05A10

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