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We present here a new approach to investigate the Kolakoski sequence Kol(a, b). In the first part of this paper, we give some general identities. In the second, we state our main result, which concerns the frequency of the letters in the case where a and b are odd. Finally, we give an algorithm to compute the term Kn in the particular case of Kol(1, 3).

Some Formulas for the Generalized Kolakoski Sequence <i>Kol</i>(<i>a, b</i>)