Could someone help me out with this? Thank you in advance!

Question 4. Let S be the set of binary strings consisting of a (nonempty) block of 0s followed by a (nonempty) block of 1s, such that if the block of Os has odd length, then the block of 1s has even length. Let an be the number of strings of length n in S (a) (b) Find ao, a1, a2, a3. Prove that s = {0)(0)'{1}{1}* \ {0)(00)'(1)(11)'. (c) Show that the generating function for S is r3 (2+x) 1-22 S(r) - (d) (e) Write down a recurrence equation for an Determine a closed formula for an for all n, and find a1o01