In this work, we define the recurrence sequence by using the relation matrix of the generalized quaternion group and then, we obtain miscellaneous properties of this sequence. Also, we obtain the cyclic groups and the semigroups which are produced by generating matrix of the sequence defined when read modulo m . Furthermore, we study this sequence modulo m, and then we derive the relationship among the order the cyclic groups obtained and the periods of the sequence defined.
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