A note on generalized Leonardo numbers

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
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Authors and affiliations

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


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.


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

2010 Mathematics Subject Classification

  • 11B37
  • 11B39


  1. 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.
  2. Sloane, N. J. A. (2019). The on-line encyclopedia of integer sequences. The OEIS
    Foundation Inc. Available online at: http://oeis.org.
  3. Horadam, A. F. (1961). A Generalized Fibonacci sequence. American Mathematical Monthly, 68 (5), 455–459.
  4. Horadam, A. F. (1965). Basic properties of a certain generalized sequence of numbers. The Fibonacci Quarterly, 3 (3), 161–176.
  5. Asveld, P. R. J. (1987). A family of Fibonacci-like sequences. The Fibonacci Quarterly, 25 (1), 81–83.
  6. 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.
  7. 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.

Related papers

  1. Vieira, R. P. M., Mangueira, M. C. S., Alves, F. R. V., & Catarino, P. M. M. C. (2021). Leonardo’s three-dimensional relations and some identities. Notes on Number Theory and Discrete Mathematics, 27(4), 32-42.

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.

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