a(n) is the number of partitions of n with Durfee square of size <= 3.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =7a(6) =11a(7) =15a(8) =22a(9) =30a(10) =42a(11) =56a(12) =77a(13) =101a(14) =135a(15) =176a(16) =230a(17) =295a(18) =380a(19) =480a(20) =607a(21) =758a(22) =943a(23) =1161a(24) =1426a(25) =1733a(26) =2100a(27) =2525a(28) =3023a(29) =3595