English

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 nnth term of the kk-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having kk arbitrary initial terms, where the succeeding terms are obtained by adding its previous kk terms. The formula for the nnth term of the kk-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 kk-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}
}
R2 v1 2026-06-28T00:52:54.323Z