**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)**

## Details

### 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*

### Abstract

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.

### Keywords

- 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).

## Related papers

- Anđelić, M., & da Fonseca, C. M. (2021). Determinantal representations for the number of subsequences without isolated odd terms.
*Notes on Number Theory and Discrete Mathematics*, 27(4), 116–121. - Deveci, Ö., & Shannon, A. G. (2022). On recurrence results from matrix transforms.
*Notes on Number Theory and Discrete Mathematics*, 28(4), 589–592. - Estrada, E., & de la Peña, J. A. (2013). Integer sequences from walks in graphs.
*Notes on Number Theory and Discrete Mathematics*, 19(3), 78–84.

## 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.