(a) For the alphabet ∑ = {0, 1}, let an count the number of strings of length n in ∑- that is, for n ∈ N, an = |∑n|. Determine the generating function for the sequence a0, a1, a2, . . . .
(b) Answer the question posed in part (a) when | ∑ | - k, a fixed positive integer.