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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =2a(5) =0a(6) =1a(7) =12a(8) =4a(9) =1a(10) =30a(11) =60a(12) =9a(13) =56a(14) =280a(15) =225a(16) =106a(17) =840a(18) =1681a(19) =852a(20) =2012a(21) =7393a(22) =8102a(23) =6116a(24) =24089a(25) =48288a(26) =39312a(27) =69889a(28) =206354a(29) =268496