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").

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

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. 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.

Crossrefs

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