Fast forwarding hash functions
Follow up to the answer (to some degree). 
Using a hash function in this way is somewhat equivalent to fast forwarding a pseudorandom number generator.
A linear congruential generator (LCG) can be skipped ahead [link], in fact many PRNG's can be skipped/jumped ahead [link]. 
The problem with fast-forwarding any hash/prng, is that if you know the cycle period (which you do with most PRNGs),
by fastforwarding the period-1, you effectively move back 1 state.  
Thus if we found a way to say move forward quickly with a SHA256, the first person to correctly estimate its cycle period would also have the ability to move backward as well.
The only fix for this is to have a system with a huge number of varied cycles.  E.g. having 256 bits worth of different cycles lengths, which each cycle being 64-256 bits in cycle length, fitting in 512 bits of state.
No known way of doing this, but should one be found, you've solved multiple comp-sci and cryptology problems, and made efficient signing of messages trivial.
tl;dr - if you can go forward and calculate its cycle length, you can go backward.