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 Let$\begin{align*} A_0 &= 6 \\ A_1 &= 5 \\ A_n &= A_{n - 1} + A_{n - 2} \; \textrm{for} \; n \geq 2. \end{align*}$.

There is a unique ordered pair (c,d) such that $c\phi^n + d\widehat{\phi}^n$ is the closed form for sequence A_n.  Find c using the Fibonacci and Lucas number