Abstract
In this paper, we describe the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the non-abelian groups and then we investigate them in non-abelian finite groups in detail. Furthermore, we give the lengths of the periods of the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the polyhedral group with respect to the generating triple as applications of the results produced.
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