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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =4a(5) =0a(6) =3a(7) =20a(8) =12a(9) =4a(10) =56a(11) =112a(12) =37a(13) =120a(14) =504a(15) =486a(16) =300a(17) =1584a(18) =3175a(19) =2124a(20) =4196a(21) =13736a(22) =16576a(23) =14560a(24) =46217a(25) =92336a(26) =87024a(27) =145226a(28) =391124a(29) =540192