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arXiv · 2304.02871

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

Martin Bunder·Joseph Tonien
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Abstract

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

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Martin Bunder, Joseph Tonien. 2023-04-06. On the linear space of the two-sided generalized Fibonacci sequences. https://arxiv.org/abs/2304.02871

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