Let
A_0 = 6
A_1 = 5
A_n = A_(n-1) + A_(n-2) for n ≥ 2
There is a unique ordered pair (c,d) such that \(c\phi^n + d\widehat{\phi}^n\) is the closed form for A_n. Find c using the Fibonacci and Lucas number sequences.
Taking the limit, we get that c = 4 - sqrt(5).
