Erzincan Binali Yıldırım ÜniversitesiErzincan Binali Yıldırım ÜniversitesiAçık Erişim Arşivi · RDL Open

A New Approach to k-Oresme and k-Oresme-Lucas Sequences

ArticleAçık Erişim

Özet

In this study, the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are presented. In addition, we give these sequences the Binet formulas, generating functions, Cassini identity, Catalan identity etc. Moreover, the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are associated with Fibonacci, Pell numbers and Lucas, and Pell- Lucas numbers, respectively. Finally, the Catalan transforms of these sequences are given and Hankel transforms are applied to these Catalan sequences and associated with the terms of the sequence. © 2024 by the authors.

Anahtar Kelimeler

generating functionOresme numbersOresme-Lucas numberssequences
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/11146Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.3390/sym16111407Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorÖzkan, Engin
dc.contributor.authorAkkuş, Hakan
dc.date.accessioned2026-10-18T20:26:14.848981112Z
dc.date.available2026-10-18T20:26:14.848981112Z
dc.date.issued2024
dc.description.abstractIn this study, the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are defined, and some terms of these sequence are given. Then, the relations between the terms of the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are presented. In addition, we give these sequences the Binet formulas, generating functions, Cassini identity, Catalan identity etc. Moreover, the (Formula presented.) -Oresme and (Formula presented.) -Oresme-Lucas sequences are associated with Fibonacci, Pell numbers and Lucas, and Pell- Lucas numbers, respectively. Finally, the Catalan transforms of these sequences are given and Hankel transforms are applied to these Catalan sequences and associated with the terms of the sequence. © 2024 by the authors.
dc.identifier.doi10.3390/sym16111407
dc.identifier.eissn2073-8994
dc.identifier.issn2073-8994
dc.identifier.issue11
dc.identifier.scopus2-s2.0-85210551409
dc.identifier.startpage1407
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/11146
dc.identifier.volume16
dc.identifier.wosWOS:001366077200001
dc.language.isoen
dc.publisherMultidisciplinary Digital Publishing Institute (MDPI)
dc.relation.ispartofSymmetry
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectgenerating function
dc.subjectOresme numbers
dc.subjectOresme-Lucas numbers
dc.subjectsequences
dc.titleA New Approach to k-Oresme and k-Oresme-Lucas Sequences
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus13
rdl.citation.wos11
rdl.oa.statusgold
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.wos.indexScience Citation Index Expanded (SCI-EXPANDED)