A326175 Number of minimal subsets of {1..n} containing n whose sum is greater than or equal to the sum of their complement.

1, 1, 1, 3, 3, 5, 10, 14, 25, 44, 71, 128, 231, 411, 740, 1352, 2481, 4570, 8390, 15550, 29103, 54345, 101312, 190316, 359827, 679051, 1279956, 2426200, 4621174, 8789565, 16701225, 31871629, 61052515, 116818123, 223333533, 428435056, 824395640, 1584833707, 3044562148, 5865073390, 11326741619, 21857561924

Offset: 1

Author

Gus Wiseman, Jun 11 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(8) = 14 subsets:
  {1}  {2}  {3}  {1,4}  {3,5}    {5,6}    {1,6,7}    {3,7,8}
                 {2,4}  {4,5}    {1,4,6}  {2,5,7}    {4,6,8}
                 {3,4}  {1,2,5}  {2,3,6}  {2,6,7}    {4,7,8}
                                 {2,4,6}  {3,4,7}    {5,6,8}
                                 {3,4,6}  {3,5,7}    {5,7,8}
                                          {3,6,7}    {6,7,8}
                                          {4,5,7}    {1,2,7,8}
                                          {4,6,7}    {1,3,6,8}
                                          {5,6,7}    {1,4,5,8}
                                          {1,2,4,7}  {2,3,5,8}
                                                     {2,3,6,8}
                                                     {2,4,5,8}
                                                     {3,4,5,8}
                                                     {1,2,3,4,8}
		

Crossrefs

Cf. A053632, A057567, A057568, A059529, A063865, A326152, A326173, A326174.

Programs

Mathematica

fasmin[y_]:=Complement[y,Union@@Table[Union[s,#]&/@Rest[Subsets[Complement[Union@@y,s]]],{s,y}]];
Table[Length[fasmin[Select[Subsets[Range[n]],MemberQ[#,n]&&Plus@@#>=Plus@@Complement[Range[n],#]&]]],{n,10}]

Extensions

a(15)-a(42) from Bert Dobbelaere, Jun 22 2019