Is fixed key AES in counter mode a PRG? I want to implement a PRG (Pseudorandom Generator). As AES is implemented in hardware, I am planning to use AES for efficiency. I am planning to use:

$(AES_k(seed) \| AES_k(seed+1) \| AES_k(seed+2) \|....)$ 

as a PRG ($k$ represents the key of AES). The receiver of this sequence does not know the random seed, but knows the AES key $k$. So, is this sequence a provably secure PRG, when the AES key is known (at least in ideal cipher model)?
Hint: given $AES_k(seed)$ and the key $k$, what can an adversary compute? Should this be possible for a secure PRG?

A better option would be standard CTR mode, i.e. $AES_{seed}(0) \| AES_{seed}(1), ...$