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

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =2a(8) =3a(9) =0a(10) =3a(11) =12a(12) =10a(13) =4a(14) =30a(15) =60a(16) =40a(17) =60a(18) =210a(19) =286a(20) =231a(21) =560a(22) =1267a(23) =1428a(24) =1722a(25) =4208a(26) =7182a(27) =8064a(28) =13275a(29) =28080