Yücel Türker Ulutaş and Derya Toy

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 2, Pages 252–260

DOI: 10.7546/nntdm.2022.28.2.252-260

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## Details

### Authors and affiliations

**Yücel Türker Ulutaş**

*Department of Mathematics, University of Kocaeli
Kocaeli, Turkey*

**Derya Toy**

*Institute of Science and Technology, University of Kocaeli
Kocaeli, Turkey*

### Abstract

In this study, we take the generalized Fibonacci sequence as and for , where is a non-zero integer. Based on Halton’s paper in [4], we derive three interrelated functions involving the terms of generalized Fibonacci sequence . Using these three functions we introduce a simple approach to obtain a lot of identities, binomial sums and alternate binomial sums involving the terms of generalized Fibonacci sequence .

### Keywords

- Generalized Fibonacci numbers
- Sums of generalized Fibonacci numbers
- Binomial sums

### 2020 Mathematics Subject Classification

- 11B37
- 11B39
- 11B65

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### Manuscript history

- Received: 4 June 2021
- Revised: 28 April 2022
- Accepted: 5 May 2022
- Online First: 6 May 2022

## Related papers

## Cite this paper

Türker Ulutaş, Y., & Toy, D. (2022). Some equalities and binomial sums about the generalized Fibonacci number *u _{n}*.

*Notes on Number Theory and Discrete Mathematics*, 28(2), 252-260, DOI: 10.7546/nntdm.2022.28.2.252-260.