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) 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 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. Ⓒ 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) . Shannon, A. G., Shiue, P. J.-S., & Saito, C. (2026). Some properties of a Padovan sequence. Notes on Number Theory and Discrete Mathematics , 32(4), 658-677, DOI: 10.7546/nntdm.2026.32.4.658-677.