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October 11th, 2013, 06:10 PM   #1
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Finding the Closed-Form Expression For a Recurrence

n is deemed to only be a power of 3.


Doing repeated substitution I get:



So this is going to keep going until becomes equal to whatever n is.
Also since n is a power of 3 we know this will be when

Therefore



Not really sure where to go from here as it seems to be a geometric series yet that really does not help me with the closed form.

Also I have tried to just work out a pattern looking at the numbers:



so the 4 and the -3i I get but not to sure how to resolve the rest.

I believe it has to do with finding closed form for a geometric series...

Any help would be appreciated!
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