THE HYPERBOLIC-TYPE k-FIBONACCI SEQUENCES AND THEIR APPLICATIONS

TAŞ S.

THERMAL SCIENCE, cilt.26, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/tsci22s2551t
  • Dergi Adı: THERMAL SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Anahtar Kelimeler: hyperbolic number, hyperbolic-type sequence, group, matrix, period, LUCAS, NUMBERS
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this study, we define hyperbolic-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the hyperbolic-type k-Fibonacci numbers. In addition, we study the hyperbolic-type k-Fibonacci sequence modulo m and then we give periods of the Hperbolic-type k-Fibonacci sequences for any k and m which are related the periods of the k-step Fibonacci sequences modulo m. Furthermore, we extend the hyperbolic-type k-Fibonacci sequences to groups. Finally, we obtain the periods of the hyperbolic-type 2-Fibonacci sequences in the dihedral group D-2m, (m >= 2) with respect to the generating pairs (x, y) and (y, x).