On the 2k-step Jordan-Fibonacci sequence
ADVANCES IN DIFFERENCE EQUATIONS, 2017 (SCI-Expanded, Scopus)
- 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.