Liviu P. DINU
On the Density of Certain Languages

Abstract.
We prove that the number of the words of length n over the alphabet {v; c} (vowel, consonant) which contain no consecutive vowels is equal to the (n + 1)th term of the Fibonacci sequence. Then, we evaluate the number of the words of length n, over the same alphabet, which contain exactly k consecutive vowels (k ≥ 1).