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ON DOUBLED AND QUADRUPLED FIBONACCI TYPE SEQUENCES

ArticleAçık Erişim

Özet

In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle. ©2023 The Author(s).

Anahtar Kelimeler

Fibonacci numbersgeneralized Fibonacci numbersgenerating functionNarayana’s numbersPadovan’s numbersPascal’s triangle
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/11297Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.2478/amsil-2023-0020Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorYilmaz, Nur Şeyma
dc.contributor.authorWłoch, Andrzej
dc.contributor.authorÖzkan, Engin
dc.contributor.authorStrzałka, Dominik
dc.date.accessioned2026-10-18T20:26:22.170307836Z
dc.date.available2026-10-18T20:26:22.170307836Z
dc.date.issued2024
dc.description.abstractIn this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled Narayana’s sequence. We give a binomial direct formula for these sequences using graph methods, and also we derive a number of identities. Moreover, we study matrix generators of these sequences and determine connections with the Pascal’s triangle. ©2023 The Author(s).
dc.identifier.doi10.2478/amsil-2023-0020
dc.identifier.eissn2391-4238
dc.identifier.endpage350
dc.identifier.issn0860-2107
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85178048510
dc.identifier.startpage336
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/11297
dc.identifier.volume38
dc.identifier.wosWOS:001108252000001
dc.language.isoen
dc.publisherSciendo
dc.relation.ispartofAnnales Mathematicae Silesianae
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectFibonacci numbers
dc.subjectgeneralized Fibonacci numbers
dc.subjectgenerating function
dc.subjectNarayana’s numbers
dc.subjectPadovan’s numbers
dc.subjectPascal’s triangle
dc.titleON DOUBLED AND QUADRUPLED FIBONACCI TYPE SEQUENCES
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus1
rdl.citation.wos1
rdl.oa.statusgold
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexEmerging Sources Citation Index (ESCI)