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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 recurrenceis probably not new, we have not been able to find a reference for it.

A fast recurrence for Fibonacci and Lucas numbers