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arXiv · 2112.10895

A fast recurrence for Fibonacci and Lucas numbers

Jeroen van de Graaf
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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.

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Jeroen van de Graaf. 2021-12-16. A fast recurrence for Fibonacci and Lucas numbers. https://arxiv.org/abs/2112.10895

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