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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## Details

### 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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## Cite this paper

Leung, H.-H. (2020). Some binomial-sum identities for the generalized bi-periodic Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 26(1), 199-208, doi: 10.7546/nntdm.2020.26.1.199-208.