Calculating coefficient of generating function with Coin

The problem I'm currently looking over requires use of generating functions to solve the following:

If a coin is flipped $25$ times with eight tails occurring, what is the probability that no run of six (or more) consecutive heads occurs?

I know that you need to designate $H$ (heads) and $T$ (tails), such as $H = 1$, $T = x$ and this would give you the binomial expression $(1+x)^n$, but I'm not entirely sure how to handle the constraint of tails already occurring and then find a probability of six (or more) consecutive heads from that.

I appreciate the help!

-