Number of integer partitions of n whose semi-sums cover an interval of positive integers.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =6a(6) =9a(7) =10a(8) =13a(9) =17a(10) =20a(11) =26a(12) =31a(13) =38a(14) =44a(15) =58a(16) =64a(17) =81a(18) =95a(19) =116a(20) =137a(21) =166a(22) =192a(23) =233a(24) =278a(25) =330a(26) =385a(27) =459a(28) =542a(29) =636