Formula for the $n$th $k$-Generalized Fibonacci-like Number
General Mathematics
2022-09-08 v1
Abstract
In this paper we provided a formula for the th term of the -generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having arbitrary initial terms, where the succeeding terms are obtained by adding its previous terms. The formula for the th term of the -generalized Fibonacci-like sequence was obtained by observing patterns in the derived formula for the nth term of the Fibonacci-like, Tribonacci-like, and Tetrabonacci-like sequence. The formula for the -generalized Fibonacci sequence was also derived and was used in the process of proving the main result of this paper.
Cite
@article{arxiv.2209.03165,
title = {Formula for the $n$th $k$-Generalized Fibonacci-like Number},
author = {John Alexis B. Gemino and Alexander J. Balsomo and Geneveve M. Parreño-Lachica and Dave Ryll B. Libre and Marc Raniel A. Nuñeza},
journal= {arXiv preprint arXiv:2209.03165},
year = {2022}
}