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a(n) counts the distinct cubical (on alphabet of 3 symbols) billiard words with length n, acting as prefix to just k = 2 such words of length n+1 (that is, a subset of "special").
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%I #9 Sep 08 2022 08:45:54

%S 0,0,6,18,36,78,150,306,420,792,1338,2082,3228,4830,7050,9954,13920,

%T 18738,24666,32610

%N a(n) counts the distinct cubical (on alphabet of 3 symbols) billiard words with length n, acting as prefix to just k = 2 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, A180439.

%K nonn,more

%O 0,3

%A _Fred Lunnon_, Sep 05 2010