a(n) is the number of vertices in the diagram of partitions of n (see example).

Terms

a(0) =1a(1) =4a(2) =7a(3) =10a(4) =16a(5) =22a(6) =34a(7) =46a(8) =67a(9) =91a(10) =127a(11) =169a(12) =232a(13) =304a(14) =406a(15) =529a(16) =694a(17) =892a(18) =1156a(19) =1471a(20) =1882a(21) =2377a(22) =3007a(23) =3766a(24) =4726a(25) =5875a(26) =7309a(27) =9031a(28) =11155a(29) =13696