Extending R. Grimaldi's work on binary strings and Ja-cobsthal numbers for the language A = {0,01,11}, we will examine some general properties for counting binary languages. We focus mainly on counts for the number of strings of length n inside the Kleene closure of a given language. We will discuss how these counts are affected when adding additional elements to a language. We also present counts for the number of 0's and 1's inside these binarystrings of length n.
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