a(n) = Sum_{k=0..floor(n/3)} Stirling2(k,n - 3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =0a(6) =0a(7) =1a(8) =1a(9) =0a(10) =1a(11) =3a(12) =1a(13) =1a(14) =7a(15) =6a(16) =2a(17) =15a(18) =25a(19) =11a(20) =32a(21) =90a(22) =66a(23) =78a(24) =302a(25) =351a(26) =267a(27) =987a(28) =1703a(29) =1305