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

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =8a(5) =0a(6) =12a(7) =80a(8) =48a(9) =32a(10) =448a(11) =896a(12) =336a(13) =1920a(14) =8064a(15) =7872a(16) =8320a(17) =50688a(18) =101824a(19) =79616a(20) =262400a(21) =879616a(22) =1096704a(23) =1490944a(24) =5888256a(25) =11923456a(26) =13332480a(27) =34886656a(28) =100288512a(29) =146227200