On the fibonacci-circulant p-sequences

Abstract

In this paper, we define the generalized Fibonacci-circulant psequence and the Fibonacci-circulant p-sequence by using the circulant matrix which is obtained from the characteristic polynomial of the Fibonacci p-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 study the orders of these groups. Furthermore, we extend the Fibonacci-circulant p-sequence to groups and then, we study this sequence in finite groups. Finally, we obtain the lengths of the periods of the Fibonacci-circulant p-orbits of the polyhedral group (2,n,2) as applications of the results obtained. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.