## Abstract

A k-nacci (k-step Fibonacci) sequence in a finite group is a sequence of group elements x_{0, 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.
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Original language | English |
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Pages (from-to) | 17-30 |

Journal | Algebra Colloquium |

Volume | 21 |

Issue number | 59 |

DOIs | |

Publication status | Published - 2014 |

## Keywords

- k-nacci sequence
- period
- modular group

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