Generalized Bronze Leonardo sequence

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Özet

In this study, we define the Bronze Leonardo, Bronze Leonardo-Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc. Also, we obtain the Binet formulas in three different ways. The first is in the known classical way, the second is with the help of the sequence's generating functions, and the third is with the help of the matrices. In addition, we find the special relations between the terms of the Bronze Leonardo, Bronze Leonardo-Lucas, and Modified Bronze Leonardo sequences. Moreover, we examine the relationships among the Bronze Fibonacci and Bronze Lucas sequences of these sequences. Finally, we associate these sequences with the matrices.

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AlanDeğerDil
dc.contributor.authorOzkan, Engin
dc.contributor.authorAkkus, Hakan
dc.date.accessioned2026-10-18T20:38:59.065124536Z
dc.date.available2026-10-18T20:38:59.065124536Z
dc.date.issued2024
dc.description.abstractIn this study, we define the Bronze Leonardo, Bronze Leonardo-Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc. Also, we obtain the Binet formulas in three different ways. The first is in the known classical way, the second is with the help of the sequence's generating functions, and the third is with the help of the matrices. In addition, we find the special relations between the terms of the Bronze Leonardo, Bronze Leonardo-Lucas, and Modified Bronze Leonardo sequences. Moreover, we examine the relationships among the Bronze Fibonacci and Bronze Lucas sequences of these sequences. Finally, we associate these sequences with the matrices.
dc.identifier.doi10.7546/nntdm.2024.30.4.811-824
dc.identifier.eissn2367-8275
dc.identifier.endpage824
dc.identifier.issn1310-5132
dc.identifier.issue4
dc.identifier.startpage811
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/16875
dc.identifier.volume30
dc.identifier.wosWOS:001367683900004
dc.language.isoen
dc.publisherBULGARIAN ACAD SCIENCE
dc.relation.ispartofNOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectLeonardo number
dc.subjectGenerating function
dc.subjectBinet formula
dc.subjectFibonacci sequence
dc.subjectMathematics
dc.titleGeneralized Bronze Leonardo sequence
dc.typeArticle
dspace.entity.typePublication
rdl.citation.wos11
rdl.oa.statusgold
rdl.source.indexWOS
rdl.wos.indexEmerging Sources Citation Index (ESCI)