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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =4a(5) =0a(6) =4a(7) =32a(8) =16a(9) =8a(10) =144a(11) =288a(12) =80a(13) =512a(14) =2304a(15) =2080a(16) =1856a(17) =12800a(18) =25664a(19) =17408a(20) =58624a(21) =204928a(22) =242944a(23) =299520a(24) =1258752a(25) =2541568a(26) =2609152a(27) =6824448a(28) =20169728a(29) =28344320