A180438 -id:A180438 - cp's OEIS frontend

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

Fred Lunnon, Sep 05 2010

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.

Fred Lunnon, Magma program

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

Magma
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A180439 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").

Original entry on oeis.org

1, 3, 3, 3, 9, 15, 33, 63, 153, 219, 261, 351, 585, 879, 933, 1233, 1401, 1899, 2301, 3111

Offset: 0

Fred Lunnon, Sep 05 2010

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.

Cf. A005598, A180238, A180239, A180437, A180438.

cp's OEIS Frontend

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").

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