On the 2k-step Jordan-Fibonacci sequence

Deveci O., TAŞ S., KILIÇMAN A.

ADVANCES IN DIFFERENCE EQUATIONS, 2017 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1186/s13662-017-1178-2
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Jordan-Fibonacci sequence, group, matrix, period, FINITE-GROUPS, PADOVAN SEQUENCES, MODULO-M
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, we define the 2k-step Jordan-Fibonacci sequence, and then we study the 2k-step Jordan-Fibonacci sequence modulo m. Also, we obtain the cyclic groups from the multiplicative orders of the generating matrix of the 2k-step Jordan-Fibonacci sequence when read modulo m, and we give the relationships among the orders of the cyclic groups obtained and the periods of the 2k-step Jordan-Fibonacci sequence modulo m. Furthermore, we extend the 2k-step Jordan-Fibonacci sequence to groups, and then we examine this sequence in the finite groups. Finally, we obtain the period of the 2k-step Jordan-Fibonacci sequence in the generalized quaternion group Q(2)n as applications of the results produced.