a(n) is the number of distinct billiard words with length n on an alphabet of 3 symbols.

Terms

a(0) =1a(1) =3a(2) =9a(3) =27a(4) =75a(5) =189a(6) =447a(7) =951a(8) =1911a(9) =3621a(10) =6513a(11) =11103a(12) =18267a(13) =29013a(14) =44691a(15) =67251a(16) =98547a(17) =140865a(18) =197679a(19) =272799a(20) =370659a(21) =497403a(22) =658371a(23) =859863a(24) =1110453a(25) =1420527a(26) =1799373a(27) =2260161a(28) =2815401a(29) =3479235