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A fast recurrence for Fibonacci and Lucas numbers

2021/12/16 by van de Graaf, Jeroen
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.10895

Abstract

We derive the double recurrence en = (1)/(2)(an-1+5bn-1); fn = (1)/(2)(an-1+bn-1) with e0=2;f0=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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