Number of integer partitions of n whose semi-sums do not cover an interval of positive integers.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =2a(7) =5a(8) =9a(9) =13a(10) =22a(11) =30a(12) =46a(13) =63a(14) =91a(15) =118a(16) =167a(17) =216a(18) =290a(19) =374a(20) =490a(21) =626a(22) =810a(23) =1022a(24) =1297a(25) =1628a(26) =2051a(27) =2551a(28) =3176a(29) =3929