a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k,n-3*k).

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =74a(5) =267a(6) =981a(7) =3648a(8) =13690a(9) =51744a(10) =196699a(11) =751237a(12) =2880345a(13) =11080081a(14) =42743148a(15) =165291569a(16) =640563158a(17) =2487083484a(18) =9672626600a(19) =37674470433a(20) =146937686295a(21) =573781535775