a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+2,2*n-6*k+1).

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =4a(5) =0a(6) =12a(7) =40a(8) =12a(9) =32a(10) =224a(11) =224a(12) =112a(13) =960a(14) =2016a(15) =1152a(16) =3600a(17) =12672a(18) =13120a(19) =15168a(20) =64256a(21) =110848a(22) =99904a(23) =291200a(24) =734912a(25) =836608a(26) =1376256a(27) =4114432a(28) =6516224a(29) =8042496