Some properties of a Padovan sequence

Anthony G. Shannon, Peter J.-S. Shiue and Christopher Saito
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 4, Pages 658–677
DOI: 10.7546/nntdm.2026.32.4.658-677
Full paper (PDF, 274 Kb)

Details

Authors and affiliations

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

Peter J.-S. Shiue
Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154-4020, USA

Christopher Saito
Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154-4020, USA

Abstract

This paper explores a connection between third order Padovan sequences and generalized continued fractions by analogy with second order recursive sequences and ordinary two-dimensional continued fractions. It does this with a partial recurrence relation which is related to the original third order Padovan relation.

Keywords

• Fibonacci numbers
• Tribonacci numbers
• Partial quotients
• Euclidean Algorithm
• Padovan sequences

2020 Mathematics Subject Classification

• 11B39
• 11Y99

References

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Manuscript history

• Received: 8 September 2026
• Revised: 23 October 2026
• Accepted: 29 October 2026
• Online First: 12 November 2026

Copyright information

Ⓒ 2026 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).