Number of partitions of n+3 with largest inscribed rectangle having area <= n.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =3a(5) =5a(6) =17a(7) =22a(8) =39a(9) =57a(10) =85a(11) =107a(12) =162a(13) =208a(14) =273a(15) =360a(16) =474a(17) =597a(18) =774a(19) =970a(20) =1233a(21) =1553a(22) =1937a(23) =2396a(24) =2991a(25) =3694a(26) =4539a(27) =5572a(28) =6822a(29) =8309