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**1. The problem statement, all variables and given/known data**

Find and prove the recurrence relation for the Fibonacci cubed sequence.

**2. Relevant equations**

By observation (blankly staring at the sequence for an hour) I've decided that the recurrence relation is G[tex]_{n}[/tex] = 3G[tex]_{n-1}[/tex] + 6G[tex]_{n-2}[/tex] - 3G[tex]_{n-3}[/tex] - G[tex]_{n-4}[/tex]

(where G is Fibonacci cubed)

**3. The attempt at a solution**

My attempt was going to be to prove by induction, but for the n+1 case, I got:

G[tex]_{n+1}[/tex] = G[tex]_{n}[/tex] + F[tex]_{n}[/tex]*F[tex]_{n+1}[/tex]*F[tex]_{n-1}[/tex] + G[tex]_{n-1}[/tex]

Is there an identity that could get me further? Is there a different method anyone could suggest? Is there anything I can do at all?

edit: all that superscript is supposed to be subscript... I'm not sure what happened...

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