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A fast recurrence for Fibonacci and Lucas numbers

12/16/2021

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by Jeroen van de Graaf, et al.

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We derive the double recurrence e_n = 1/2(a_n-1+5b_n-1); f_n = 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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