Counting number of strings that contain substring matching Regular Expression

Counting number of strings that contain substring matching Regular Expression

I have regular expression R. And I want to find the F(n) is the number of
strings of length n that strings that contain substring matching Regular
Expression. Suppose the alphabet-size is M.
We can apply the generating function to compute the number of strings of
length n that matches R, but i can't find any answer for the above
question.
Do you have any idea on that?