Hacène Belbachir and Ihab-Eddine Djellas
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 64—74
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Recently companion sequences of -Fibonacci sequence were defined. The aim of this paper is to give some determinantal and permanental representations of these sequences via Hessenberg matrices. Several representations of classical sequences and polynomials are established. We conclude by using our representations to give consecutive terms of companion sequences simultaneously.
- Generalized bivariate r-Fibonacci polynomials
- Generalized bivariate r-Lucas polynomials
- Companion sequences
- Hessenberg matrix
2020 Mathematics Subject Classification
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- Received: 22 January 2021
- Revised: 24 November 2021
- Accepted: 11 February 2022
- Online First: 14 February 2022
Cite this paper
Belbachir, H., & Djellas, I.-E. (2022). Determinantal and permanental representations of companion sequences associated to the r-Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 28(1), 64-74, DOI: 10.7546/nntdm.2022.28.1.64-74.