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GENERALIZED FIBONACCI NUMBERS WITH FIVE PARAMETERS

ArticleAçık Erişim

Özet

In this paper, we define five parameters generalization of Fibonacci numbers that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana, Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci numbers, gen-eralized (k, r)-Fibonacci numbers in the distance sense by extending the defini-tion of a distance in the recurrence relation with two parameters and adding three parameters in the definition of this distance, simultaneously. Tiling and combinatorial interpretations of generalized Fibonacci numbers are presented, and explicit formulas that allow us to calculate the nth number are given. Also generating functions and some identities for these numbers are obtained. © 2022 Society of Thermal Engineers of Serbia

Anahtar Kelimeler

combinatorial identitiesdistance Fibonacci numbersgeneralized Fibonacci numberssums formulastilingsCombinatorial identityDistance fibonacci numberFibonacci numbersFive parametersGeneralized fibonacci numberJacobsthal numbersParameter generalizationSum formulaTilingNumber theory
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/12984Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.2298/tsci22s2495tYayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorTasyurdu, Yasemin
dc.date.accessioned2026-10-18T20:27:50.245860174Z
dc.date.available2026-10-18T20:27:50.245860174Z
dc.date.issued2022
dc.description.abstractIn this paper, we define five parameters generalization of Fibonacci numbers that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana, Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci numbers, gen-eralized (k, r)-Fibonacci numbers in the distance sense by extending the defini-tion of a distance in the recurrence relation with two parameters and adding three parameters in the definition of this distance, simultaneously. Tiling and combinatorial interpretations of generalized Fibonacci numbers are presented, and explicit formulas that allow us to calculate the nth number are given. Also generating functions and some identities for these numbers are obtained. © 2022 Society of Thermal Engineers of Serbia
dc.identifier.doi10.2298/tsci22s2495t
dc.identifier.eissn2334-7163
dc.identifier.endpageS505
dc.identifier.issn0354-9836
dc.identifier.issueSpecialIssue2
dc.identifier.scopus2-s2.0-85148224162
dc.identifier.startpageS495
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/12984
dc.identifier.volume26
dc.identifier.wosWOS:000921231700001
dc.language.isoen
dc.publisherSerbian Society of Heat Transfer Engineers
dc.relation.ispartofThermal Science
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectcombinatorial identities
dc.subjectdistance Fibonacci numbers
dc.subjectgeneralized Fibonacci numbers
dc.subjectsums formulas
dc.subjecttilings
dc.subjectCombinatorial identity
dc.subjectDistance fibonacci number
dc.subjectFibonacci numbers
dc.subjectFive parameters
dc.subjectGeneralized fibonacci number
dc.subjectJacobsthal numbers
dc.subjectParameter generalization
dc.subjectSum formula
dc.subjectTiling
dc.subjectNumber theory
dc.titleGENERALIZED FIBONACCI NUMBERS WITH FIVE PARAMETERS
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus1
rdl.citation.wos1
rdl.oa.statusgold
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexScience Citation Index Expanded (SCI-EXPANDED)