On the bivariate Padovan polynomials matrix

Orhan Dişkaya, Hamza Menken and Paula Maria Machado Cruz Catarino
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 407–420
DOI: 10.7546/nntdm.2023.29.3.407-420
Full paper (PDF, 237 Kb)

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Authors and affiliations

Orhan Dişkaya
Department of Mathematics, Mersin University
Mersin, Turkey

Hamza Menken
Department of Mathematics, Mersin University
Mersin, Turkey

Paula Maria Machado Cruz Catarino
Department of Mathematics, University of Trás-os-Montes and Alto Douro
Vila Real, Portugal

Abstract

In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate Padovan polynomials matrix. Also, we obtain a sum formula and its series representation.

Keywords

• Padovan numbers
• Padovan polynomials
• Binet-like formula
• Generating function
• Bivariare polynomials
• Matrix

2020 Mathematics Subject Classification

• 11B39
• 05A15

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Manuscript history

• Received: 9 October 2022
• Revised: 24 March 2023
• Accepted: 28 May 2023
• Online First: 5 June 2023

Copyright information

Ⓒ 2023 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).