%N a(n) counts the distinct cubical (on alphabet of 3 symbols) billiard words with length n, acting as prefix to just k = 3 such words of length n+1 (that is, a subset of "special").
%C By symmetry under reversal, a(n) also counts length n cubical billiard words acting as suffix to just k length n+1 cubical billiard words. Computation: _Fred Lunnon_ for 0 <= n <= 19 (MAGMA). The program in A180437 counts k-special words for k = 1,...,m, where m = 3 denotes the size of the alphabet.
%Y Cf. A005598, A180238, A180239, A180437, A180438.
%A _Fred Lunnon_, Sep 05 2010