(adsbygoogle = window.adsbygoogle || []).push({}); 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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# Fibonacci Cubed Recurrence Relation

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