OFFSET
0,4
COMMENTS
Also the number of minimal subsets of {1..n} whose sum is greater than or equal to the sum of their complement. For example, the a(0) = 1 through a(7) = 16 subsets are:
{} {1} {2} {3} {1,4} {3,5} {5,6} {1,6,7}
{1,2} {2,3} {4,5} {1,4,6} {2,5,7}
{2,4} {1,2,5} {2,3,6} {2,6,7}
{3,4} {1,3,4} {2,4,5} {3,4,7}
{2,3,4} {2,4,6} {3,5,6}
{3,4,5} {3,5,7}
{3,4,6} {3,6,7}
{1,2,3,5} {4,5,6}
{4,5,7}
{4,6,7}
{5,6,7}
{1,2,4,7}
{1,2,5,6}
{1,3,4,6}
{2,3,4,5}
{2,3,4,6}
EXAMPLE
The a(0) = 1 through a(7) = 16 subsets:
{} {} {1} {3} {1,2} {1,5} {4,6} {1,5,7}
{1,2} {1,3} {2,5} {1,2,5} {1,6,7}
{1,4} {3,4} {1,2,6} {2,5,7}
{2,3} {1,2,3} {1,3,5} {3,4,7}
{1,2,4} {1,3,6} {3,5,6}
{1,4,5} {1,2,3,4}
{2,3,5} {1,2,3,5}
{1,2,3,4} {1,2,3,6}
{1,2,3,7}
{1,2,4,5}
{1,2,4,6}
{1,2,4,7}
{1,2,5,6}
{1,3,4,5}
{1,3,4,6}
{2,3,4,5}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Plus@@Complement[Range[n], #]>=Plus@@#&]]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2019
EXTENSIONS
a(16)-a(42) from Bert Dobbelaere, Jun 22 2019
STATUS
approved