The Fibonacci-circulant sequences in the binary polyhedral groups

In ۲۰۱۷ Deveci et al‎. ‎defined the Fibonacci-circulant sequences of the first and second kinds as shown‎, ‎respectively:‎x_n^۱ = -x_(n-۱)^۱+x_(n-۲)^۱-x_(n-۳)^۱ for n≥۴,where x_۱^۱=x_۲^۱=۰ and x_۳^۱=۱andx_n^۲ = -x_(n-۳)^۲-x_(n-۴)^۲+x_(n-۵)^۲ for n≥۶,where x_۱^۲=x_۲^۲=x_۳^۲=x_۴^۲=۰ and x_۵^۲=۱‎Also‎, ‎they extended the Fibonacci-circulant sequences of the first and second kinds to groups‎. ‎In this paper‎, ‎we obtain the periods of the Fibonacci-circulant sequences of the first and second kinds in the binary polyhedral groups‎.

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The Fibonacci-circulant sequences ، Period ، group