This note can be viewed as a logical continuation of our previous Note published earlier in the Monthly 1]. We shall repeat here, brieey, its main results to make the reading easier. A counting sequence S is a sequence of sequences fS i g 1 i=0 of positive integers. The sequence S i+1 is obtained from S i by counting the number m k of times an integer k occurs in S i and writing down in S i+1 t...

The Danish composer Per Nørg̊ard defined the “infinity series” s = (s(n))n≥0 by the rules s(0) = 0, s(2n) = −s(n) for n ≥ 1, and s(2n + 1) = s(n) + 1 for n ≥ 0; it figures prominently in many of his compositions. Here we give several new results about this sequence: first, the set of binary representations of the positions of each note forms a context-free language that is not regular; second, a...