A note on Q-matrices and higher order Fibonacci polynomials

Paolo Emilio Ricci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 1, Pages 91—100
DOI: 10.7546/nntdm.2021.27.1.91-100
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Authors and affiliations

Paolo Emilio Ricci
Section of Mathematics, International Telematic University UniNettuno
Corso Vittorio Emanuele II, 39, 00186, Roma, Italia

Abstract

The results described in a recent article, relative to a representation formula for the generalized Fibonacci sequences in terms of Q-matrices are extended to the case of Fibonacci, Tribonacci and R-bonacci polynomials.

Keywords

• Fibonacci numbers
• Tribonacci polynomials
• R-bonacci polynomials
• Q-matrices
• Matrix powers.

2010 Mathematics Subject Classification

• Primary 11B39
• Secondary 11B83, 12E10, 65Q30, 15A24

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