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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =6a(5) =0a(6) =9a(7) =72a(8) =36a(9) =27a(10) =486a(11) =972a(12) =297a(13) =2592a(14) =11664a(15) =10611a(16) =13446a(17) =97200a(18) =195129a(19) =149688a(20) =663876a(21) =2334987a(22) =2838726a(23) =4697676a(24) =21485817a(25) =43705008a(26) =51438240a(27) =171480483a(28) =517850982a(29) =760446144