I'm trying to solve this recurrence equation in this way:
$$ T(0)=O(1)\\ T(n) = 2T(n - 1) + n \\ = 2[ 2T(n - 2) + (n - 1) ] + n \\ = 2[ 2[ 2T( n - 3 ) + ( n - 2 ) ] + ( n - 1 ) ] + n \\ = 2³T(n-3) + 2²(n-2) + 2(n-1) + n$$
And I get:
$$ \sum_{i=0}^{n} 2^i(n-i) $$
That's right?