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A326175
Number of minimal subsets of {1..n} containing n whose sum is greater than or equal to the sum of their complement.
6
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
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2019
EXTENSIONS
a(15)-a(42) from Bert Dobbelaere, Jun 22 2019
STATUS
approved