Counting Clean Words According to the Number of Their Clean Neighbors

We extract brilliant ideas of Sandi Klavzar, Michel Mollard, and Marko Petkovsek who used them to solve one very specific enumeration problem, namely counting the number of words in the alphabet {0,1} of length n avoiding two consecutive ones, and having exactly k such neighbors, to a much more general setting where one has any (finite) alphabet, and any (finite) set of forbidden subwords. More important, we fully implement it in Maple.