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A Study on the k-Mersenne and k-Mersenne-Lucas Sequences

ArticleAçık Erişim

Özet

In this study, we examine an application of k−Mersenne and k−Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of k−Mersenne and k−Mersenne-Lucas sequences have terms according to different values of k, and some of them are associated with the sequences in OEIS. We obtain the generating functions of the Catalan transforms of k−Mersenne and k−Mersenne-Lucas sequences. Moreover, we apply the Hankel transform to the Catalan transforms of these sequences. Finally, the determinants of the created matrices are calculated by applying the Hankel transform to the terms of the Catalan transforms of these sequences. © 2025, Emrah Evren KARA. All rights reserved.

Anahtar Kelimeler

Catalan numbersFibonacci numbersGenerating functionsHankel transformk-Mersenne se-quencesk-Mersenne-Lucas sequences
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/11348Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.32323/ujma.1566270Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorÖzkan, Engin
dc.contributor.authorŞen, Bayram
dc.contributor.authorAkkuş, Hakan
dc.contributor.authorUysal, Mine
dc.date.accessioned2026-10-18T20:26:24.862091931Z
dc.date.available2026-10-18T20:26:24.862091931Z
dc.date.issued2025
dc.description.abstractIn this study, we examine an application of k−Mersenne and k−Mersenne-Lucas sequences. We present the Catalan transforms of these sequences and give the properties of these Catalan transforms. Catalan transforms of k−Mersenne and k−Mersenne-Lucas sequences have terms according to different values of k, and some of them are associated with the sequences in OEIS. We obtain the generating functions of the Catalan transforms of k−Mersenne and k−Mersenne-Lucas sequences. Moreover, we apply the Hankel transform to the Catalan transforms of these sequences. Finally, the determinants of the created matrices are calculated by applying the Hankel transform to the terms of the Catalan transforms of these sequences. © 2025, Emrah Evren KARA. All rights reserved.
dc.identifier.doi10.32323/ujma.1566270
dc.identifier.endpage7
dc.identifier.issn2619-9653
dc.identifier.issue1
dc.identifier.scopus2-s2.0-105001512742
dc.identifier.startpage1
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/11348
dc.identifier.volume8
dc.language.isoen
dc.publisherEmrah Evren KARA
dc.relation.ispartofUniversal Journal of Mathematics and Applications
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectCatalan numbers
dc.subjectFibonacci numbers
dc.subjectGenerating functions
dc.subjectHankel transform
dc.subjectk-Mersenne se-quences
dc.subjectk-Mersenne-Lucas sequences
dc.titleA Study on the k-Mersenne and k-Mersenne-Lucas Sequences
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus3
rdl.oa.statusgold
rdl.source.indexSCOPUS