φ = 1+sqrt(5)/2

F:fibonacci-binet(n) = Fb(n)=
  (φ^n - (-φ)^-n)/sqrt(5) =
  ((1+sqrt(5))^n - (1-sqrt(5))^n)/sqrt(5)*2^n

F(a,b,n) = (a)(Fb(n-2))+(b)(Fb(n-1)) =
  (a)((φ^(n-2) - (-φ)^(n-2))/sqrt(5)) + (b)((φ^(n-1) - (-φ)^(n-1))/sqrt(5)) =
  (a)(((1+sqrt(5))^(n-2) - (1-sqrt(5))^(n-2))/sqrt(5)*2^(n-2)) + (b)(((1+sqrt(5))^(n-1) - (1-sqrt(5))^(n-1))/sqrt(5)*2^(n-1))