Number of partitions of n having depth 3; see Comments.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =1a(8) =0a(9) =0a(10) =1a(11) =2a(12) =1a(13) =3a(14) =1a(15) =10a(16) =6a(17) =6a(18) =13a(19) =15a(20) =20a(21) =30a(22) =30a(23) =64a(24) =61a(25) =85a(26) =99a(27) =153a(28) =170a(29) =184