A note on a bivariate Leonardo sequence

Carlos M. da Fonseca and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 1, Pages 73–78
DOI: 10.7546/nntdm.2025.31.1.73-78
Full paper (PDF, 160 Kb)

Details

Authors and affiliations

Carlos M. da Fonseca
¹ Kuwait College of Science and Technology
Doha District, Safat 13133, Kuwait
² Chair of Computational Mathematics, University of Deusto
48007 Bilbao, Spain

Anthony G. Shannon
³ Honorary Fellow, Warrane College, University of New South Wales
Kensington NSW 2033, Australia

Abstract

Recently, quite a few generalizations of Leonardo numbers have emerged in the literature. In this short note, we propose a new bivariate extension and provide its generating function. We correct the generating function of another recently proposed bivariate generalization.

Keywords

• Leonardo sequence
• Generating function
• Recurrence relations
• Hessenberg matrices
• Determinant

2020 Mathematics Subject Classification

• 15A15
• 11B39

References

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Manuscript history

• Received: 19 June 2024
• Revised: 4 April 2025
• Accepted: 6 April 2025
• Online First: 7 April 2025

Copyright information

Ⓒ 2025 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).