University of Isfahan International Journal of Group Theory 2251-7650 10 3 2021 09 01 The Fibonacci-circulant sequences in the binary polyhedral groups 97 101 24424 10.22108/ijgt.2020.120894.1593 EN Erdal Karaduman Department of Mathematics, Faculty of Science, Atatürk University, 25240, Erzurum, TURKEY Omur Deveci Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100, Kars, TURKEY Journal Article 2020 01 02 In 2017 Deveci et al‎. ‎defined the Fibonacci-circulant sequences of the first and second kinds as shown‎, ‎respectively:‎<br />$x_n^1 = -x_(n-1)^1+x_(n-2)^1-x_(n-3)^1$ for $n≥4$,where $x_1^1=x_2^1=0$ and $x_3^1=1$ <br /><br />and<br /><br />$x_n^2 = -x_(n-3)^2-x_(n-4)^2+x_(n-5)^2 for n≥6$, where $x_1^2=x_2^2=x_3^2=x_4^2=0$ and $x_5^2=1$<br />‎Also‎, ‎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. https://ijgt.ui.ac.ir/article_24424_6fb9bc09ebef2c7face22edab770c98b.pdf