Simple but good

Here's a problem that I found out in an olympiad book......and I really enjoyed solving it.

The question is :

Find the sum of the given expression :

[n+12] + [n+22²] + [n+2²2³] + ................ + [n+2^k2^k+1]

where [.] denotes the greatest integer function.

Hint : This is not at all tough...but you need to know a small theorem. If no posts are there in the next 2 days...I'll post the theorem too.