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 sequences.

waffles
Feb 14, 2018