Some aspects of interchanging difference equation orders

Anthony G. Shannon and Engin Özkan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 507–516
DOI: 10.7546/nntdm.2022.28.3.507-516
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Authors and affiliations

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

Engin Özkan
Department of Mathematics, Erzincan Binali Yildirim University
Erzincan, Turkey


This paper builds on Roettger and Williams’ extensions of the primordial Lucas sequence to consider some relations among difference equations of different orders. This paper utilises some of their second and third order recurrence relations to provide an excursion through basic second order sequences and related third order recurrence relations with a variety of numerical illustrations which demonstrate that mathematical notation is a tool of thought.


  • Arbitrary order recurrence relations
  • Primordial sequences
  • Vandermonde determinants

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 11B50


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Manuscript history

  • Received: 6 June 2022
  • Revised: 28 July 2022
  • Accepted: 3 August 2022
  • Online First: 4 August 2022

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Cite this paper

Shannon, A. G., & Özkan, E. (2022). Some aspects of interchanging difference equation orders. Notes on Number Theory and Discrete Mathematics, 28(3), 507-516, DOI: 10.7546/nntdm.2022.28.3.507-516.

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