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?