Interesting. Something I didn't realize: for n > 4, F(n) = F(n-2) * 3 - F(n-4)

fibonacci sequence is defined as: F(n) = F(n-1) + F(n-2)

substitute F(n-1) with F(n-2) + F(n-3): F(n) = F(n-2) + F(n-3) + F(n-2)

substitute F(n-3) with F(n-4) + F(n-5): F(n) = F(n-2) + F(n-5) + F(n-4) + F(n-2)

substitute F(n-4) with F(n-2) - F(n-3): F(n) = F(n-2) + F(n-5) + F(n-2) - F(n-3) + F(n-2)

simplify: F(n) = 3 * F(n-2) + F(n-5) - F(n-3)

because F(n-3) = F(n-4) + F(n-5), -F(n-4) = F(n-5)) - F(n-3):

F(n) = 3 * F(n-2) - F(n-4)