Work

On the sequences of $(q,k)$-generalized Fibonacci numbers

Year: 2024

Type: article

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.

Source: Mathematica Bohemica

DOI: 10.21136/mb.2024.0036-23

Authors: Jean Lelis, Gersica Freitas, Alessandra Kreutz, Elaine Silva

Language: English

Topic: Advanced Mathematical Theories and Applications

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405416139

FWCI: 0.148

Cites: 4

Cited by: 1

Related to: 10