a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(k,3*(n-2*k)).

Terms

a(0) =1a(1) =0a(2) =2a(3) =0a(4) =3a(5) =0a(6) =4a(7) =4a(8) =5a(9) =20a(10) =6a(11) =60a(12) =7a(13) =140a(14) =15a(15) =280a(16) =65a(17) =504a(18) =262a(19) =840a(20) =851a(21) =1330a(22) =2322a(23) =2090a(24) =5557a(25) =3520a(26) =12026a(27) =6864a(28) =24052a(29) =15470