The Pell-circulant sequences and their applications (original) (raw)

The generalised order-k Pell-circulant sequence and the k-step Pell-circulant sequence are defined by using the circulant matrix which is obtained from the characteristic polynomial of the generalised order-k Pell sequence. Then the relations among the elements of the sequences and generating matrices of the sequences are obtained. Also, the cyclic groups which are generated by the generating matrices and the auxiliary equations of the defined recurrence sequences are considered, and then the orders of these groups are examined. Furthermore, the k-step Pell-circulant sequence is extended to groups. Finally, the periods of the k-step Pell-circulant sequences in the generalised quaternion group 2 n Q are obtained as applications of the results produced.