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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 453750, 10 pages
Research Article

K-nacci Sequences in Finite Triangle Groups

Department of Mathematics, Faculty of Sicence, Atatürk University, 25240 Erzurum, Turkey

Received 10 March 2009; Revised 16 July 2009; Accepted 14 September 2009

Academic Editor: Leonid Shaikhet

Copyright © 2009 Erdal Karaduman and Ömür Deveci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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,,xj1 , each element is defined by xn=x0x1xn1,for jn<k,andxn=xnkxnk+1xn1,for nk. We also require that the initial elements of the sequence, x0,x1,x2,,xj1, 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,,xj1 is denoted by Fk(G;x0,x1,,xj1) and its period is denoted by Pk(G;x0,x1,,xj1) . In this paper, we obtain the period of K-nacci sequences in finite polyhedral groups and the extended triangle groups.