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

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =8a(5) =0a(6) =16a(7) =128a(8) =64a(9) =64a(10) =1152a(11) =2304a(12) =768a(13) =8192a(14) =36864a(15) =33792a(16) =55296a(17) =409600a(18) =823296a(19) =704512a(20) =3719168a(21) =13123584a(22) =16351232a(23) =33619968a(24) =160890880a(25) =329515008a(26) =436731904a(27) =1695809536a(28) =5182586880a(29) =7935623168