Determinantal representations for the number of subsequences without isolated odd terms

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
Full paper (PDF, 157 Kb)

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

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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