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# Let

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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 sequences.

waffles  Feb 14, 2018
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