[supernewton]

> If a and b are the golden ratio and its conjugate, then f_n = a^n + b^n. But since |b| < 1, you can just do f_n = nearest_integer(a^n).

Well, almost. You need to multiply by a factor of 1/sqrt(5) before rounding.

[srean]

I sketched an alternative accurate way to the calculations here https://news.ycombinator.com/item?id=36952832 It is not faster though.