A fast recurrence for Fibonacci and Lucas numbers

Jeroen van de Graaf

A fast recurrence for Fibonacci and Lucas numbers

Number Theory 2021-12-22 v1 Discrete Mathematics

Authors: Jeroen van de Graaf

Abstract

We derive the double recurrence $e_n = \frac{1}{2}(a_{n-1}+5b_{n-1}); f_{n} = \frac{1}{2}(a_{n-1}+b_{n-1})$ with $e_0=2;f_0=0$ for the Fibonacci numbers, leading to an extremely simple and fast implementation. Though the recurrence is probably not new, we have not been able to find a reference for it.

Keywords

fibonacci numbers lucas numbers recurrence relation fast computation

Cite

@article{arxiv.2112.10895,
  title  = {A fast recurrence for Fibonacci and Lucas numbers},
  author = {Jeroen van de Graaf},
  journal= {arXiv preprint arXiv:2112.10895},
  year   = {2021}
}

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