On Binomial Transforms: A Study of All Horadam-Type Sequences
Küçük Resim Yok
Tarih
2025
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Prof. Dr. Mehmet Zeki SARIKAYA
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This 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.
Açıklama
Anahtar Kelimeler
Binet formula, Binomial transforms, Horadam sequence
Kaynak
Konuralp Journal of Mathematics
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
13
Sayı
2
