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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =6a(5) =0a(6) =1a(7) =20a(8) =20a(9) =1a(10) =42a(11) =140a(12) =57a(13) =72a(14) =504a(15) =673a(16) =254a(17) =1320a(18) =3697a(19) =2796a(20) =3212a(21) =13729a(22) =20802a(23) =14612a(24) =40873a(25) =103232a(26) =105616a(27) =128129a(28) =391222a(29) =637840