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I cannot help myself, but I don't get the closed term for: $f(n) = n + 2 f(n-1)$, where f(1) = 1. I tried to find the pattern when looking at some iterations, and I think I see the pattern very clearly:

$...(6 + 2 ( 5 + 2 ( 4 + 2 ( 3 +2 ( 2 \cdot 1 ) ) ) ) ... )$

It's always n, reduced by the iteration plus two times the next iteration.

Any hints or what construct I should use to find the term?

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    OEIS: http://oeis.org/search?q=1,4,11,26,57,120,247,502,1013,2036&sort=number&language=english&go=Search (I made some misleading comment before, ignore it)2011-12-09

3 Answers 3