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arXiv · 2211.08941

On the Sequences of $(q,k)$-Generalized Fibonacci Numbers

Gérsica Freitas·Alessandra Kreutz·Jean Lelis·Elaine Silva
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Abstract

In this paper, we consider the new family of recurrence sequences of $(q,k)$-generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of $k$-generalized Fibonacci numbers and generalized $k$-order Pell numbers. We shall obtain a Binet-style formula and study the asymptotic behavior of dominant root of characteristic equation. Moreover, we shall prove some auxiliary results about these sequences. In particular, we characterize the first $(q,k)$-generalized Fibonacci numbers in terms of binary sequences.

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Gérsica Freitas, Alessandra Kreutz, Jean Lelis, Elaine Silva. 2022-11-16. On the Sequences of $(q,k)$-Generalized Fibonacci Numbers. https://arxiv.org/abs/2211.08941

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