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oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/111462026-10-18T20:36:44Zopenairedrivercom_ebyu_10000col_ebyu_10001

A New Approach to k-Oresme and k-Oresme-Lucas SequencesÖzkan, EnginAkkuş, Hakangenerating functionOresme numbersOresme-Lucas numberssequencesIn 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.Multidisciplinary Digital Publishing Institute (MDPI)2024Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/11146https://doi.org/10.3390/sym161114072073-8994enSymmetryinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/11146