On Binomial Transforms: A Study of All Horadam-Type Sequences

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dc.contributor.authorKaplan, Faruk
dc.contributor.authorÖztürk, Arzu Özkoç
dc.date.accessioned2026-07-01T11:36:37Z
dc.date.available2026-07-01T11:36:37Z
dc.date.issued2025
dc.departmentDüzce Üniversitesi
dc.description.abstractThis article establishes general recurrence relations, including the binomial transform, for all integer sequences with a second-order recurrence relation commonly studied in the literature. We introduce a new generalization of binomial transforms for Horadam-type sequences and investigate the binomial, k−binomial, falling k−binomial, and rising k−binomial transforms on these sequences. Additionally, we derive the corresponding recurrence relations, Binet formulas, generating functions and Pascal’s triangle for each of the four transforms. © 2025, Prof. Dr. Mehmet Zeki SARIKAYA. All rights reserved.
dc.identifier.dergipark1704831
dc.identifier.endpage211
dc.identifier.issn2147-625X
dc.identifier.issue2
dc.identifier.scopus2-s2.0-105022914327
dc.identifier.scopusqualityQ3
dc.identifier.startpage198
dc.identifier.urihttps://hdl.handle.net/20.500.12684/23142
dc.identifier.volume13
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherProf. Dr. Mehmet Zeki SARIKAYA
dc.relation.ispartofKonuralp Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_Scopus_20260623
dc.subjectBinet formula
dc.subjectBinomial transforms
dc.subjectHoradam sequence
dc.titleOn Binomial Transforms: A Study of All Horadam-Type Sequences
dc.typeArticle

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