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Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different sum.
15

%I #5 Jun 02 2019 23:40:39

%S 1,1,1,1,4,5,8,22,40,56,78,124,222,390,616,892,1220,1620,2182,3042,

%T 4392

%N Number of maximal subsets of {1..n} such that every orderless pair of distinct elements has a different sum.

%e The a(1) = 1 through a(6) = 8 subsets:

%e {1} {1,2} {1,2,3} {1,2,3} {1,2,4} {1,2,3,5}

%e {1,2,4} {2,3,4} {1,2,3,6}

%e {1,3,4} {2,4,5} {1,2,4,6}

%e {2,3,4} {1,2,3,5} {1,3,4,5}

%e {1,3,4,5} {1,3,5,6}

%e {1,4,5,6}

%e {2,3,4,6}

%e {2,4,5,6}

%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];

%t Table[Length[fasmax[Select[Subsets[Range[n]],UnsameQ@@Plus@@@Subsets[Union[#],{2}]&]]],{n,0,10}]

%Y The subset case is A196723.

%Y The maximal case is A325878.

%Y The integer partition case is A325857.

%Y The strict integer partition case is A325877.

%Y Heinz numbers of the counterexamples are given by A325991.

%Y Cf. A002033, A108917, A143823, A143824, A276024.

%Y Cf. A325858, A325859, A325864, A325865, A325867, A325879, A325880.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Jun 02 2019