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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =2a(5) =0a(6) =5a(7) =20a(8) =4a(9) =7a(10) =70a(11) =84a(12) =17a(13) =168a(14) =504a(15) =299a(16) =346a(17) =1848a(18) =2653a(19) =1452a(20) =5180a(21) =13743a(22) =12350a(23) =14508a(24) =51561a(25) =81440a(26) =68432a(27) =162323a(28) =391026a(29) =442544