TY - JOUR
TI - The hyperbolic-type k-Fibonacci sequences and their applications
AU - Tas Sait
JN - Thermal Science
PY - 2022
VL - 26
IS - 102
SP - 551
EP - 558
PT - Article
AB - 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 D2m, (m ≥ 2) with respect to the generating pairs (x,y) and  (y, x).