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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =3a(5) =0a(6) =1a(7) =15a(8) =15a(9) =2a(10) =36a(11) =126a(12) =85a(13) =75a(14) =495a(15) =925a(16) =600a(17) =1431a(18) =5007a(19) =6588a(20) =6063a(21) =19020a(22) =43983a(23) =49743a(24) =72829a(25) =206826a(26) =363495a(27) =428528a(28) =852102a(29) =1999155