Number of subsets of {1..n} containing at least one element that is a sum of distinct non-elements.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =4a(5) =13a(6) =33a(7) =81a(8) =183a(9) =402a(10) =856a(11) =1801a(12) =3721a(13) =7646a(14) =15567a(15) =31575a(16) =63767a(17) =128520a(18) =258353a(19) =518843a(20) =1040564a(21) =2085635a(22) =4177405a(23) =8364464a(24) =16741825a(25) =33504005a(26) =67035250a(27) =134112744a(28) =268282800a(29) =536654110