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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =8a(5) =15a(6) =39a(7) =119a(8) =328a(9) =867a(10) =2375a(11) =6644a(12) =18479a(13) =51259a(14) =142947a(15) =400308a(16) =1122344a(17) =3150219a(18) =8858019a(19) =24948026a(20) =70348943a(21) =198585320a(22) =561176440a(23) =1587368782a(24) =4494028879a(25) =12733338015a(26) =36105583059a(27) =102449288109a(28) =290886486227a(29) =826416320732