Number of partitions p of n such that floor(mean(p)) is a part and ceiling(mean(p)) is not.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =1a(7) =3a(8) =4a(9) =6a(10) =9a(11) =16a(12) =11a(13) =29a(14) =36a(15) =38a(16) =51a(17) =89a(18) =81a(19) =145a(20) =134a(21) =191a(22) =278a(23) =369a(24) =290a(25) =520a(26) =678a(27) =768a(28) =875a(29) =1320