Calculate the number of distinct permutations of length n in the closure of a language I am studying a distance CS course, but there is no tutor available, so I would appreciate your help...

Consider the language $S = \{a, aa, ab\}$
How many distinct words of length $n$ will appear in $S^*$?

Is there a way to do this without having to "enumerate" $S^*$ until the answer is found?
The language $S^*$ is regular.  Therefore, it can be expressed by a DFA.  Now use Why isn&#39;t it simple to count the number of words in a regular language? or https://cstheory.stackexchange.com/q/8200/5038.