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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =2a(5) =0a(6) =4a(7) =16a(8) =4a(9) =8a(10) =72a(11) =72a(12) =24a(13) =256a(14) =576a(15) =288a(16) =816a(17) =3200a(18) =3264a(19) =3104a(20) =14432a(21) =25728a(22) =20672a(23) =58752a(24) =157120a(25) =173184a(26) =257152a(27) =809600a(28) =1296000a(29) =1466368