Bi-periodic $r$-Fibonacci sequence and bi-periodic $r$-Lucas sequence of type $s$

DOI10.15672/hujms.825908OpenAlexW4210318865MaRDI QIDQ5057391

Hacène Belbachir, N. Rosa Ait-Amrane

Publication date: 16 December 2022

Published in: Hacettepe Journal of Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.15672/hujms.825908

zbMATH Keywords

generating functionrecurrence relationexplicit formulacompanion sequenceBinet formbi-periodic \(r\)-Fibonacci sequencebi-periodic \(r\)-Lucas sequence

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Binomial coefficients; factorials; (q)-identities (11B65) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Numerical aspects of recurrence relations (65Q30)

Cites Work

• Two generalizations of Lucas sequence
• Suites récurrentes linéaires. Propriétés algébriques et arithmétiques. (Linear recurrent sequences. Algebraic and arithmetic properties)
• A note on generalized Fibonacci sequences
• A New Generalization of Fibonacci Sequence & Extended Binet's Formula
• Companion sequences associated to ther-Fibonacci sequence: algebraic andcombinatorial properties
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