The Fibonacci-Circulant Sequences and their Applications

Document Type : Regular Paper


1 Kafkas University

2 Department of Mathematics, Faculty of Science, Atatürk University.

3 School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland.


In this paper, we define the recurrence sequences by using the circulant matrices which are obtained from the characteristic polynomial of the Fibonacci sequence. Then we obtain miscellaneous properties of these sequences. Also, we consider the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences and then we examine the orders of these groups. Furthermore, we extend the defined sequences to groups. Finally, we obtain the lengths of the periods of the extended sequences in the polyhedral groups (2,3,3) and (n,2,2) as applications of the results obtained.


Main Subjects