On the Pell p-circulant sequences

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Journal Article
Notes on Number Theory and Discrete Mathematics, 2017, 23 (2), pp. 91 - 103
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In this paper, we define the generalized Pell p-circulant sequence and the Pell pcirculant sequence by using the circulant matrices which are obtained from the characteristic polynomial of the generalized Pell ( p,i)-sequence and 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 Pell p-circulant sequence to groups. Finally, we obtain the lengths of the periods of Pell p-circulant sequences in the semidihedral group 2 SD m for m ≥ 4 as applications of the results obtained.
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