Merve Taştan and Engin Özkan

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 1, Pages 198–207

DOI: 10.7546/nntdm.2021.27.1.198-207

**Full paper (PDF, 865 Kb)**

## Details

### Authors and affiliations

Merve Taştan

*Graduate School of Natural and Applied Sciences
Erzincan Binali Yıldırım University
24100 Erzincan, Turkey*

Engin Özkan

*Graduate School of Natural and Applied Sciences
Erzincan Binali Yıldırım University
24100 Erzincan, Turkey*

### Abstract

In this study, we present the Catalan transforms of the *k*-Pell sequence, the *k*-Pell–Lucas sequence and the Modified *k*-Pell sequence and examine the properties of the sequences. Then we apply the Hankel transform to the Catalan transforms of the *k*-Pell sequence, the Catalan transform of the *k*-Pell–Lucas sequence and the Catalan transform of the Modified *k*-Pell sequence. Also, we obtain the generating functions of the Catalan transform of the *k*-Pell sequence, *k*-Pell–Lucas sequence and Modified *k*-Pell sequence. Furthermore, we acquire an interesting characteristic related to the determinant of the Hankel transform of the sequences.

### Keywords

*k*-Pell numbers*k*-Pell–Lucas- Catalan numbers
- Catalan transform
- Hankel transform

### 2010 Mathematics Subject Classification

- 11B39
- 11B83
- 11C20

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## Cite this paper

Taştan, M. & Özkan, E. (2021). Catalan transform of the *k*-Pell, *k*-Pell–Lucas and modified *k*-Pell sequence. *Notes on Number Theory and Discrete Mathematics*, 27(1), 198-207, DOI: 10.7546/nntdm.2021.27.1.198-207.