a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,3*n-6*k+2).

Terms

a(0) =1a(1) =0a(2) =3a(3) =0a(4) =6a(5) =0a(6) =10a(7) =1a(8) =15a(9) =6a(10) =21a(11) =21a(12) =28a(13) =56a(14) =37a(15) =126a(16) =54a(17) =252a(18) =100a(19) =462a(20) =231a(21) =793a(22) =573a(23) =1299a(24) =1378a(25) =2080a(26) =3108a(27) =3367a(28) =6556a(29) =5733