Catalan transform of the k-Pell, k-Pell–Lucas and modified
k-Pell sequence

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)

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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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