Some binomial-sum identities for the generalized bi-periodic Fibonacci sequences

Ho-Hon Leung
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 199-208
DOI: 10.7546/nntdm.2020.26.1.199-208
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Authors and affiliations

Ho-Hon Leung
Department of Mathematical Sciences, United Arab Emirates University
Al-Ain, United Arab Emirates

Abstract

A bi-periodic sequence is a sequence which satisfies different recurrence relations
depending on whether the n-th term considered is odd or even. In this paper, we investigate the properties of the generalized bi-periodic Fibonacci sequences. It is a generalization of the biperiodic Fibonacci sequences defined by Edson and Yayenie. We derive binomial-sum identities or the generalized bi-periodic Fibonacci sequences by matrix method. Our identities generalize binomial-sum identities derived by Edson and Yayenie for the case of bi-periodic Fibonacci sequences.

Keywords

• Fibonacci sequence
• Matrix method
• Binomial sum

2010 Mathematics Subject Classification

• 11B39
• 05A15

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