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

Terms

a(0) =1a(1) =0a(2) =3a(3) =2a(4) =15a(5) =24a(6) =86a(7) =192a(8) =546a(9) =1381a(10) =3651a(11) =9582a(12) =24901a(13) =65748a(14) =170796a(15) =450017a(16) =1172412a(17) =3080367a(18) =8044478a(19) =21096027a(20) =55169988a(21) =144535714a(22) =378243264a(23) =990489234a(24) =2592800365a(25) =6788471991a(26) =17771977254a(27) =46527959417a(28) =121812102840a(29) =318906184152