Milica Anđelic and Carlos M. da Fonseca

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 116—121

DOI: 10.7546/nntdm.2021.27.4.116-121

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## Details

### Authors and affiliations

Milica Anđelic

*Department of Mathematics, Kuwait University
Safat 13060, Kuwait*

Carlos M. da Fonseca

*Kuwait College of Science and Technology
Doha District, Safat 13133, Kuwait*

*Chair of Computational Mathematics, University of Deusto*

48007 Bilbao, Basque Country, Spain

48007 Bilbao, Basque Country, Spain

### Abstract

In this short note we propose two determinantal representations for the number of subsequences without isolated odd terms are presented. One is based on a tridiagonal matrix and other on a Hessenberg matrix. We also establish a new explicit formula for the terms of this sequence based on Chebyshev polynomials of the second kind.

### Keywords

- Tridiagonal 2-Toeplitz matrices
- Determinant
- Hessenberg matrices
- Chebyshev polynomials of the second kind
- Recurrence relation

### 2020 Mathematics Subject Classification

- 11B37
- 11B39
- 15B36
- 15A15

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## Cite this paper

Anđelic, 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, doi: 10.7546/nntdm.2021.27.4.116-121.