English

A simplified Binet formula for k-generalized Fibonacci numbers

Number Theory 2022-02-25 v2

Abstract

We present a particularly nice Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula to generate the desired sequence. These results were also found (independently) at about the same time by Zhaohui Du of Singapore, China. We are working on a joint paper.

Keywords

Cite

@article{arxiv.0905.0304,
  title  = {A simplified Binet formula for k-generalized Fibonacci numbers},
  author = {Gregory P. Dresden},
  journal= {arXiv preprint arXiv:0905.0304},
  year   = {2022}
}

Comments

8 pages, bibliography

R2 v1 2026-06-21T12:57:46.212Z