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

1,4

Links

Table of n, a(n) for n=1..42.

Example

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}

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}]

Crossrefs

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

Sequence in context: A294617 A320450 A100886 * A072337 A335056 A132751

Adjacent sequences: A326172 A326173 A326174 * A326176 A326177 A326178

Keyword

nonn

Author

Gus Wiseman, Jun 11 2019

Extensions

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

Status

approved