On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence

Carlos M. da Fonseca and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 557–563
DOI: 10.7546/nntdm.2023.29.3.557-563
Full paper (PDF, 350 Kb)


Authors and affiliations

Carlos M. da Fonseca
Kuwait College of Science and Technology,
Doha District, Safat 13133, Kuwait
Chair of Computational Mathematics, University of Deusto
48007 Bilbao, Spain

Anthony G. Shannon
Honorary Fellow, Warrane College, University of New South Wales, 2033, Australia


Recently, based on the Laplace transform of the characteristic polynomial of the Fibonacci sequence, Deveci and Shannon established a new sequence and analysed some of its properties. They disclosed in particular the odd terms. In this short note, we provide a matricial representation for this sequence as well as one in terms of the Chebyshev polynomials of the second kind. The subsequence of the even terms is also disclosed.


  • Fibonacci sequence
  • Recurrence
  • Chebyshev polynomials of the second kind
  • Determinant
  • Tridiagonal matrices

2020 Mathematics Subject Classification

  • 11B37
  • 11B39
  • 15A15


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Manuscript history

  • Received: 11 February 2023
  • Revised: 18 July 2023
  • Accepted: 29 July 2023
  • Online First: 30 July 2023

Copyright information

Ⓒ 2023 by the Authors.
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).

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Cite this paper

Da Fonseca, C. M., & Shannon, A. G. (2023). On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 29(3), 557-563, DOI: 10.7546/nntdm.2023.29.3.557-563.

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