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A325878
Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different sum.
15
1, 1, 1, 1, 4, 5, 8, 22, 40, 56, 78, 124, 222, 390, 616, 892, 1220, 1620, 2182, 3042, 4392
OFFSET
0,5
EXAMPLE
The a(1) = 1 through a(6) = 8 subsets:
{1} {1,2} {1,2,3} {1,2,3} {1,2,4} {1,2,3,5}
{1,2,4} {2,3,4} {1,2,3,6}
{1,3,4} {2,4,5} {1,2,4,6}
{2,3,4} {1,2,3,5} {1,3,4,5}
{1,3,4,5} {1,3,5,6}
{1,4,5,6}
{2,3,4,6}
{2,4,5,6}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], UnsameQ@@Plus@@@Subsets[Union[#], {2}]&]]], {n, 0, 10}]
CROSSREFS
The subset case is A196723.
The maximal case is A325878.
The integer partition case is A325857.
The strict integer partition case is A325877.
Heinz numbers of the counterexamples are given by A325991.
Sequence in context: A275929 A240794 A171938 * A352396 A072808 A104884
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jun 02 2019
STATUS
approved