A New Approach to k-Oresme and k-Oresme-Lucas Sequences

ÖZKAN E., Akkuş H.

Symmetry, cilt.16, sa.11, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 11
  • Basım Tarihi: 2024
  • Doi Numarası: 10.3390/sym16111407
  • Dergi Adı: Symmetry
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: generating function, Oresme numbers, Oresme-Lucas numbers, sequences
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

In 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.