Number of compositions minus number of partitions: A011782(n) - A000041(n).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =9a(6) =21a(7) =49a(8) =106a(9) =226a(10) =470a(11) =968a(12) =1971a(13) =3995a(14) =8057a(15) =16208a(16) =32537a(17) =65239a(18) =130687a(19) =261654a(20) =523661a(21) =1047784a(22) =2096150a(23) =4193049a(24) =8387033a(25) =16775258a(26) =33551996a(27) =67105854a(28) =134214010a(29) =268430891