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

Terms

a(0) =1a(1) =0a(2) =0a(3) =8a(4) =16a(5) =0a(6) =48a(7) =320a(8) =192a(9) =256a(10) =3584a(11) =7168a(12) =3328a(13) =30720a(14) =129024a(15) =129024a(16) =245760a(17) =1622016a(18) =3272704a(19) =3293184a(20) =16596992a(21) =56360960a(22) =74776576a(23) =166985728a(24) =752156672a(25) =1552941056a(26) =2268069888a(27) =8638693376a(28) =25806503936a(29) =41498443776