On some combinations of k-nacci numbers

Pavel Trojovský

Chaos, Solitons & Fractals, 2016, vol. 85, issue C, 135-137

Abstract: For k ≥ 2, the k-generalized Fibonacci sequence (Fn(k))n is defined by the initial values 0,0,…,0,1 (k terms) and such that each term afterwards is the sum of the k preceding terms. In this paper, we shall study for which x, k and t the expression xtFn+t(k)+⋯+xFn+1(k)+Fn(k) belongs to (Fm(k))m for infinitely many integers n. This work generalizes [13, Theorem 2] which is related to the case t=1.

Keywords: Combination; Recurrence sequence; k-generalized Fibonacci sequence (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:85:y:2016:i:c:p:135-137

DOI: 10.1016/j.chaos.2016.01.028

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