a(n) = 3^n(n^2 - n + 18)/18.

Terms

a(0) =1a(1) =3a(2) =10a(3) =36a(4) =135a(5) =513a(6) =1944a(7) =7290a(8) =26973a(9) =98415a(10) =354294a(11) =1259712a(12) =4428675a(13) =15411789a(14) =53144100a(15) =181752822a(16) =617003001a(17) =2080591515a(18) =6973568802a(19) =23245229340a(20) =77096677311a(21) =254535261273a(22) =836828256240