a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(4*k,n-3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =16a(5) =30a(6) =39a(7) =175a(8) =784a(9) =2100a(10) =4590a(11) =13970a(12) =50743a(13) =153634a(14) =408499a(15) =1187823a(16) =3843280a(17) =11908160a(18) =34470084a(19) =101394222a(20) =313440606a(21) =967143586a(22) =2897603170a(23) =8660763804a(24) =26408966551a(25) =80995131580a(26) =245801163530a(27) =742776778965