**A. G. Shannon**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 3, Pages 97–101

DOI: 10.7546/nntdm.2019.25.3.97-101

**Full paper (PDF, 98 Kb)**

## Details

### Authors and affiliations

A. G. Shannon

*Warrane College, The University of New South Wales,
Kensington, NSW 2033, Australia
*

### Abstract

This is essentially an expository paper which sheds new light on existing knowledge due to Asveld and Horadam and suggests ideas for extension and generalization based on the approaches of these authors.

### Keywords

- Fibonacci sequence
- Pell sequence
- Homogeneous and inhomogeneous recurrence relations
- Pascal’s triangle

### 2010 Mathematics Subject Classification

- 11B37
- 11B39

### References

- Catarino, P., & Borges, A. (2019). On Leonardo numbers. Acta Mathematica

Universitatis Comenianae, 1–12. Available online at: http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1005/650. - Sloane, N. J. A. (2019). The on-line encyclopedia of integer sequences. The OEIS

Foundation Inc. Available online at: http://oeis.org. - Horadam, A. F. (1961). A Generalized Fibonacci sequence. American Mathematical Monthly, 68 (5), 455–459.
- Horadam, A. F. (1965). Basic properties of a certain generalized sequence of numbers. The Fibonacci Quarterly, 3 (3), 161–176.
- Asveld, P. R. J. (1987). A family of Fibonacci-like sequences. The Fibonacci Quarterly, 25 (1), 81–83.
- Horadam, A. F., & Shannon, A. G. (1988). Asveld’s polynomials. In
*Philippou, A.N., Horadam, A.F. & Bergum, G. E. (eds). Applications of Fibonacci Numbers, Volume 2*. Dordrecht: Kluwer, 163–176. - Bondarenko, B. A. (1993). Generalized Pascal Triangles and Pyramids: Their Fractals, Graphs and Applications. (Translated by R. C. Bollinger.) Santa Clara, CA: The Fibonacci Association.

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*Notes on Number Theory and Discrete Mathematics*, 28(1), 109-114, DOI: 10.7546/nntdm.2022.28.1.109-114. - Shattuck, M. (2022). Combinatorial proofs of identities for the generalized Leonardo numbers.
*Notes on Number Theory and Discrete Mathematics*, 28(4), 778-790. - Shannon, A. G., Shiue, P. J.-S., & Huang, S. C. (2023). Notes on generalized and extended Leonardo numbers.
*Notes on Number Theory and Discrete Mathematics*, 29(4), 752-773. - Arpacı, S., & Yılmaz, F. (2024). Some results on geometric circulant matrices involving the Leonardo numbers.
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## Cite this paper

Shannon, A. G. (2019). A note on generalized Leonardo numbers. *Notes on Number Theory and Discrete Mathematics*, 25(3), 97-101, DOI: 10.7546/nntdm.2019.25.3.97-101.