Another six Fibonacci-like sequences

Karol Gryszka
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 3, Pages 563–569
DOI: 10.7546/nntdm.2025.31.3.563-569
Full paper (PDF, 182 Kb)

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Authors and affiliations

Karol Gryszka
Institute of Mathematics
University of the National Education Commission, Krakow
Podchorążych 2, 30-084 Kraków, Poland

Abstract

We briefly describe six Fibonacci-like sequences or arbitrary order that give rise to a periodic or eventually periodic sequences. We provide some examples and demonstrate the explicit periods of these sequences.

Keywords

• Arbitrary order recurrence relation
• Fibonacci sequence
• Periodic sequence

2020 Mathematics Subject Classification

• 11B39

References

1. Atanassov, K. T., & Shannon, A. G. (2025). Two Fibonacci-like sequences. Notes on Number Theory and Discrete Mathematics, 31(2), 335–339.
2. Gryszka, K. (2022). A note on the Fibonacci m-step sequences modulo q. Mathematical Communications, 27(2), 215–223.
3. Philippou, A. N. (1983). A note on the Fibonacci sequence of order k and the multinomial coefficients. The Fibonacci Quarterly, 21(2), 82–86.
4. Shannon, A. G. (1976). Some number theoretic properties of arbitrary order recursive sequences. Bulletin of the Australian Mathematical Society, 14(1), 149–151.

Manuscript history

• Received: 9 June 2025
• Revised: 4 August 2025
• Accepted: 20 August 2025
• Online First: 21 August 2025

Copyright information

Ⓒ 2025 by the Author.
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).