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

Terms

a(0) =1a(1) =0a(2) =1a(3) =5a(4) =18a(5) =66a(6) =246a(7) =924a(8) =3493a(9) =13277a(10) =50697a(11) =194327a(12) =747319a(13) =2882061a(14) =11142027a(15) =43167573a(16) =167561586a(17) =651513594a(18) =2537041938a(19) =9892847952a(20) =38623197264a(21) =150959213886a(22) =590626854072