A three by three Pascal matrix representations of the generalized Fibonacci and Lucas sequences

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dc.contributor.authorKoken, Fikri
dc.date.accessioned2024-02-23T14:32:07Z
dc.date.available2024-02-23T14:32:07Z
dc.date.issued2020
dc.departmentNEÜen_US
dc.description.abstractIn this study, a matrix R-v is defined, and two closed form expressions of the matrix R-v(n), for an integer n >= 1, are evaluated by the matrix functions in matrix theory. These expressions satisfy a connection between the generalized Fibonacci and Lucas numbers with the Pascal matrices. Thus, two representations of the matrix R-v(n) and various forms of matrix (R-v +q Delta I)(n) are studied in terms of the generalized Fibonacci and Lucas numbers and binomial coefficients. By modifying results of 2 x 2 matrix representations given in the references of our study, we give various 3 x 3 matrix representations of the generalized Fibonacci and Lucas sequences. Many combinatorial identities are derived as applications.en_US
dc.identifier.doi10.15672/hujms.481026
dc.identifier.endpage1743en_US
dc.identifier.issn2651-477X
dc.identifier.issue5en_US
dc.identifier.scopus2-s2.0-85092935168en_US
dc.identifier.startpage1735en_US
dc.identifier.urihttps://doi.org/10.15672/hujms.481026
dc.identifier.urihttps://hdl.handle.net/20.500.12452/15500
dc.identifier.volume49en_US
dc.identifier.wosWOS:000581099500016en_US
dc.identifier.wosqualityQ3en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherHacettepe Univ, Fac Scien_US
dc.relation.ispartofHacettepe Journal Of Mathematics And Statisticsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectGeneralized Fibonacci And Lucas Sequencesen_US
dc.subjectGeneralized Fibonacci And Lucas Matricesen_US
dc.subjectPascal Matricesen_US
dc.titleA three by three Pascal matrix representations of the generalized Fibonacci and Lucas sequencesen_US
dc.typeArticleen_US

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