The k-Nacci Sequences in Some Special Modular Groups.

A k-nacci (k-step Fibonacci) 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 From the definition, it is clear that the period of the k-nacci sequence in a group depends on the chosen generating set and the order in which the assignments of x0, x1, x2, ..., xj-1 are made. In this paper we examine the periods of the k-nacci sequences in the groups 픐2, and ℜ2, where each term of the sequence is reduced modulo 2. [ABSTRACT FROM AUTHOR]