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A326173
Number of maximal subsets of {1..n} whose sum is less than or equal to the sum of their complement.
6
1, 1, 1, 2, 4, 5, 8, 16, 24, 44, 77, 133, 240, 429, 772, 1414, 2588, 4742, 8761, 16273, 30255, 56392, 105581, 198352, 373228, 703409, 1329633, 2519927, 4781637, 9084813, 17298255, 33001380, 63023204, 120480659, 230702421, 442423139, 849161669, 1631219288, 3137595779, 6042247855, 11644198080, 22455871375, 43351354727
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
The non-maximal case is A059529.
Sequence in context: A293536 A274796 A160967 * A045591 A045581 A253426
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 11 2019
EXTENSIONS
a(16)-a(42) from Bert Dobbelaere, Jun 22 2019
STATUS
approved