On the Sequences of $(q,k)$-Generalized Fibonacci Numbers
Number Theory
2022-11-17 v1
Abstract
In this paper, we consider the new family of recurrence sequences of -generalized Fibonacci numbers. These sequences naturally extend the well-known sequences of -generalized Fibonacci numbers and generalized -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 -generalized Fibonacci numbers in terms of binary sequences.
Keywords
Cite
@article{arxiv.2211.08941,
title = {On the Sequences of $(q,k)$-Generalized Fibonacci Numbers},
author = {Gérsica Freitas and Alessandra Kreutz and Jean Lelis and Elaine Silva},
journal= {arXiv preprint arXiv:2211.08941},
year = {2022}
}