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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =2a(5) =2a(6) =8a(7) =14a(8) =20a(9) =46a(10) =92a(11) =158a(12) =314a(13) =630a(14) =1176a(15) =2274a(16) =4498a(17) =8674a(18) =16804a(19) =32990a(20) =64358a(21) =125414a(22) =245832a(23) =481674a(24) =942912a(25) =1850122a(26) =3633220a(27) =7133730a(28) =14020694a(29) =27578954