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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## Details

### 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
*

### Abstract

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.

### Keywords

- 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

## Related papers

- Frontczak, R. (2019). Relations for generalized Fibonacci and Tribonacci sequences.
*Notes on Number Theory and Discrete Mathematics*, 25(1), 178–192.

## 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.