English

On the linear space of the two-sided generalized Fibonacci sequences

Number Theory 2023-04-07 v1 Combinatorics

Abstract

In this paper, we study the linear space of all two-sided generalized Fibonacci sequences {Fn}nZ\{F_n\}_{n \in \mathbb{Z}} that satisfy the recurrence equation of order kk: Fn=Fn1+Fn2++FnkF_n = F_{n-1} + F_{n-2} + \dots + F_{n-k}. We give two types of explicit formula, one is based on generalized binomial coefficients and the other based on generalized multinomial coefficients.

Keywords

Cite

@article{arxiv.2304.02871,
  title  = {On the linear space of the two-sided generalized Fibonacci sequences},
  author = {Martin Bunder and Joseph Tonien},
  journal= {arXiv preprint arXiv:2304.02871},
  year   = {2023}
}