Abstract
The k-generalized Fibonacci sequence is the linear recurrent sequence of order k, whose first k terms are and each term afterwards is the sum of the preceding k terms. In this paper, we extend to negative indices and give an upper bound on the absolute value of its largest zero in terms of k. In particular, we find that the zero-multiplicity of the k-generalized Fibonacci sequence is exactly for all . We prove that the zero multiplicity of the k-generalized Fibonacci sequence is at least for all .
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