On some identities for the DGC Leonardo sequence

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dc.authorid0000-0002-1598-9902
dc.authorid0000-0002-8647-1801
dc.contributor.authorYilmaz, Cigdem Zeynep
dc.contributor.authorSacli, Gulsum Yeliz
dc.date.accessioned2026-04-04T18:56:12Z
dc.date.available2026-04-04T18:56:12Z
dc.date.issued2024
dc.departmentİstanbul Bilgi Üniversitesi
dc.description.abstractIn this study, we examine the Leonardo sequence with dual-generalized complex (DGC) coefficients for p is an element of R. Firstly, we express some summation formulas related to the DGC Fibonacci, DGC Lucas, and DGC Leonardo sequences. Secondly, we present some order-2 characteristic relations, involving d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities. The essential point of the paper is that one can reduce the calculations of the DGC Leonardo sequence by considering p. This generalization gives the dual-complex Leonardo sequence for p = -1, hyper-dual Leonardo sequence for p = 0, and dual-hyperbolic Leonardo sequence for p = 1.
dc.description.sponsorshipTUBITAK BIDEB 2209-A University Students Research Projects Support Program 2022 1st Term (The Scientific and Technological Research Council of Turkey-Directorate of Science Fellowships and Grant Programmes) [1919B012203959]
dc.description.sponsorshipThis work has been supported by TUBITAK BIDEB 2209-A University Students Research Projects Support Program 2022 1st Term (The Scientific and Technological Research Council of Turkey-Directorate of Science Fellowships and Grant Programmes) under support number 1919B012203959.
dc.identifier.doi10.7546/nntdm.2024.30.2.253-270
dc.identifier.doi10.7546/nntdm.2024.30.2.253-270
dc.identifier.endpage270
dc.identifier.issn1310-5132
dc.identifier.issn2367-8275
dc.identifier.issue2
dc.identifier.startpage253
dc.identifier.urihttps://doi.org/10.7546/nntdm.2024.30.2.253-270
dc.identifier.urihttps://hdl.handle.net/11411/10741
dc.identifier.volume30
dc.identifier.wosWOS:001247880700004
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.language.isoen
dc.publisherBulgarian Acad Science
dc.relation.ispartofNotes on Number Theory and Discrete Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260402
dc.subjectBinet'S Formula
dc.subjectLeonardo Numbers
dc.subjectDual -Generalized Complex Numbers.
dc.titleOn some identities for the DGC Leonardo sequence
dc.typeArticle

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