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

Terms

a(0) =1a(1) =0a(2) =2a(3) =3a(4) =3a(5) =12a(6) =9a(7) =30a(8) =35a(9) =67a(10) =111a(11) =161a(12) =296a(13) =420a(14) =728a(15) =1103a(16) =1764a(17) =2802a(18) =4313a(19) =6897a(20) =10588a(21) =16691a(22) =25830a(23) =40137a(24) =62365a(25) =96225a(26) =149235a(27) =229840a(28) =354936a(29) =546400