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

0,4

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

Table of n, a(n) for n=0..19.

Fred Lunnon, Magma program

Prog

(Magma) // See Links.

Crossrefs

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

Sequence in context: A225383 A257956 A341364 * A276179 A162583 A259662

Adjacent sequences: A180434 A180435 A180436 * A180438 A180439 A180440

Keyword

nonn,more

Author

Fred Lunnon, Sep 05 2010

Status

approved