Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 453750, 10 pages
doi:10.1155/2009/453750

$K$-nacci sequences in finite triangle groups.

Abstract

A k-nacci sequence in a finite group is a sequence of group elements x0,x1,x2,…,xn,… for which, given an initial (seed) set x0,x1,x2,…,xj−1 , each element is defined by xn=x0x1…xn−1, for   j≤n<k,  and  xn=xn−kxn−k+1…xn−1, for   n≥k. We also require that the initial elements of the sequence, x0,x1,x2,…,xj−1, generate the group, thus forcing the k-nacci sequence to reflect the structure of the group. The K-nacci sequence of a group generated by x0,x1,x2,…,xj−1 is denoted by Fk(G;x0,x1,…,xj−1) and its period is denoted by Pk(G;x0,x1,…,xj−1) . In this paper, we obtain the period of K-nacci sequences in finite polyhedral groups and the extended triangle groups.