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Boletim da Sociedade Paranaense de Matemática
Article . 2025 . Peer-reviewed
License: CC BY
Data sources: Crossref
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On the structure and generalization of bihyperbolic Leonardo sequences

descriptionPublicationkeyboard_double_arrow_right Article 02 Sep 2025Publisher:Sociedade Paranaense de MatemáticaJournal:Boletim da Sociedade Paranaense de Matemática (issn: 0037-8712, eissn: 2175-1188, Copyright policy )
Authors: Hasan Gökbaş; Anetta Szynal-Liana;

doi: 10.5269/bspm.77488

On the structure and generalization of bihyperbolic Leonardo sequences

Abstract

In this paper, we give some properties of the bihyperbolic Leonardo numbers, among others the Binet formula, generating function formula and the general bilinear index-reduction formula which implies d'Ocagne, Vajda, Halton, Catalan, and Cassini identities. We also give the matrix representation and some sum formulas of the bihyperbolic Leonardo numbers. Moreover, we present a one-parameter generalization of the bihyperbolic Leonardo numbers and their properties.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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