Some properties of Padovan matrices and bi-periodic Padovan matrices

Diana Savin
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 3, Pages 632–641
DOI: 10.7546/nntdm.2026.32.3.632-641
Full paper (PDF, 237 Kb)

Details

Authors and affiliations

Diana Savin
Faculty of Mathematics and Computer Science, Transilvania University of Brașov
50, Iuliu Maniu Str., Brașov 500091, România

Abstract

Let be the sequence of bi-periodic Padovan numbers and let be the sequence of bi-periodic Padovan matrices. In this article we study when these matrices are diagonalizable and we obtain a certain connection with the Lucas number sequence. We also obtain some connections of these matrices with the generating matrix for the Padovan numbers. At the end, we obtain an infinite cyclic subgroup of the real Heisenberg group.

Keywords

• Difference equations
• Padovan numbers
• Padovan matrices
• Bi-periodic Padovan numbers
• Bi-periodic Padovan matrices
• Diagonalizable matrices

2020 Mathematics Subject Classification

• 11B39
• 11B75
• 05C50
• 05B10
• 15A18

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Manuscript history

• Received: 29 March 2026
• Revised: 28 October 2026
• Accepted: 2 November 2026
• Online First: 3 November 2026

Copyright information

Ⓒ 2026 by the Author.
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).