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.
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