A180437 a(n) counts the distinct cubical (on alphabet of 3 symbols) billiard words with length n, acting as prefix to just k = 1 such word of length n+1 (that is, not "special").

0, 0, 0, 6, 24, 78, 186, 372, 876, 1632, 3024, 5310, 8496, 13344, 21186, 31878, 46752, 66936, 94800, 130194

Offset: 0

Author

Fred Lunnon, Sep 05 2010

Keywords

• nonn
• more

Comments

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. The attached program counts k-special words for k = 1,...,m, where m = 3 denotes the size of the alphabet.

Links

• Fred Lunnon, Magma program

Crossrefs

Cf. A005598, A180238, A180239, A180438, A180439.

Programs

Magma

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