The complex-type Pell p-numbers

Yeşim Aküzüm, Hüseyin Aydın and Ömür Deveci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 4, Pages 745–754
DOI: 10.7546/nntdm.2024.30.4.745-754
Full paper (PDF, 245 Kb)

Details

Authors and affiliations

Yeşim Aküzüm
Department of Mathematics, Faculty of Science and Letters,
Kafkas University 36100, Türkiye

Hüseyin Aydın
Department of Mathematics and Science Education, Education Faculty,
Biruni University, Istanbul, Türkiye

Ömür Deveci
Department of Mathematics, Faculty of Science and Letters,
Kafkas University 36100, Türkiye

Abstract

In this paper, we define the complex-type Pell p-numbers and give the generating matrix of these defined numbers. Then, we produce the combinatorial representation, the generating function, the exponential representation and the sums of the complex-type Pell p-numbers. Also, we derive the determinantal and the permanental representations of the complex-type Pell p-numbers by using certain matrices which are obtained from the generating matrix of these numbers. Finally, we obtain the Binet formula for the complex-type Pell p-number.

Keywords

• Pell -number
• Matrix
• Representation
• Binet formula

2020 Mathematics Subject Classification

• 11K31
• 39B32
• 15A15
• 11C20

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Manuscript history

• Received: 13 August 2024
• Revised: 7 November 2024
• Accepted: 8 November 2024
• Online First: 12 November 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).