a(3n+k) = (k+1)*binomial(4n+k, n)/(3n+k+1), where k is n reduced mod 3.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =4a(7) =9a(8) =15a(9) =22a(10) =52a(11) =91a(12) =140a(13) =340a(14) =612a(15) =969a(16) =2394a(17) =4389a(18) =7084a(19) =17710a(20) =32890a(21) =53820a(22) =135720a(23) =254475a(24) =420732a(25) =1068012a(26) =2017356a(27) =3362260a(28) =8579560a(29) =16301164