Zehra İşbilir and Nurten Gürses

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 1, Pages 171–187

DOI: 10.7546/nntdm.2021.27.1.171-187

**Full paper (PDF, 247 Kb)**

## Details

### Authors and affiliations

Zehra İşbilir

*Duzce University, Faculty of Arts and Sciences,
Department of Mathematics, 81620, Duzce, Turkey
*

Nurten Gürses

*Yildiz Technical University, Faculty of Arts and Sciences,
Department of Mathematics, 34220, Istanbul, Turkey
*

### Abstract

The aim of this article is to introduce Pell–Padovan generalized quaternions. It also derives new properties associated with these and takes into account negative indices. Additionally, it presents generating function, Binet-like formula, Simson formula, matrix representations, and several summation properties.

### Keywords

- Pell–Padovan numbers
- Generalized quaternions
- Generating function
- Binet-like formula
- Simson formula

### 2010 Mathematics Subject Classification

- 11B37
- 11C20
- 11K31
- 11R52

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## Cite this paper

İşbilir, Z., & Gürses, N. (2021). Pell–Padovan generalized quaternions. *Notes on Number Theory and Discrete Mathematics*, 27(1), 171-187, DOI: 10.7546/nntdm.2021.27.1.171-187.