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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =4a(5) =0a(6) =21a(7) =56a(8) =36a(9) =165a(10) =660a(11) =858a(12) =1729a(13) =7280a(14) =14280a(15) =23868a(16) =81396a(17) =203490a(18) =364287a(19) =975821a(20) =2699004a(21) =5492630a(22) =12728430a(23) =35036820a(24) =79616745a(25) =176181525a(26) =459439344a(27) =1117259220a(28) =2500176536a(29) =6173109360