On the linear space of the two-sided generalized Fibonacci sequences
Abstract
In this paper, we study the linear space of all two-sided generalized Fibonacci sequences \Fn\n ∈ Z that satisfy the recurrence equation of order k: Fn = Fn-1 + Fn-2 + … + Fn-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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