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%I #16 Mar 24 2022 17:34:50
%S 1,2,3,5,7,12,16,27,37,58,80,131,171,277,380,580,785,1250,1655,2616,
%T 3516,5344,7257,11353,14931,23204,31379,47511,63778,98681,130503,
%U 201357,270038,407429,548090,840171,1110429,1701872,2284325,3440337,4601656
%N Number of subsets of {1..n} containing all of their pairwise sums <= n.
%C The summands are allowed to be equal. The case where they must be distinct is A326080. If A007865 counts sum-free sets, this sequence counts sum-closed sets. This is different from sum-full sets (A093971).
%C From _Gus Wiseman_, Jul 08 2019: (Start)
%C Also the number of subsets of {1..n} containing no sum of any multiset of the elements. For example, the a(0) = 1 through a(6) = 16 subsets are:
%C {} {} {} {} {} {} {}
%C {1} {1} {1} {1} {1} {1}
%C {2} {2} {2} {2} {2}
%C {3} {3} {3} {3}
%C {2,3} {4} {4} {4}
%C {2,3} {5} {5}
%C {3,4} {2,3} {6}
%C {2,5} {2,3}
%C {3,4} {2,5}
%C {3,5} {3,4}
%C {4,5} {3,5}
%C {3,4,5} {4,5}
%C {4,6}
%C {5,6}
%C {3,4,5}
%C {4,5,6}
%C (End)
%H Fausto A. C. Cariboni, <a href="/A326083/b326083.txt">Table of n, a(n) for n = 0..100</a>
%F For n > 0, a(n) = A103580(n) + 1.
%e The a(0) = 1 through a(6) = 16 subsets:
%e {} {} {} {} {} {} {}
%e {1} {2} {2} {3} {3} {4}
%e {1,2} {3} {4} {4} {5}
%e {2,3} {2,4} {5} {6}
%e {1,2,3} {3,4} {2,4} {3,6}
%e {2,3,4} {3,4} {4,5}
%e {1,2,3,4} {3,5} {4,6}
%e {4,5} {5,6}
%e {2,4,5} {2,4,6}
%e {3,4,5} {3,4,6}
%e {2,3,4,5} {3,5,6}
%e {1,2,3,4,5} {4,5,6}
%e {2,4,5,6}
%e {3,4,5,6}
%e {2,3,4,5,6}
%e {1,2,3,4,5,6}
%e The a(7) = 27 subsets:
%e {} {4} {36} {246} {2467} {24567} {234567} {1234567}
%e {5} {45} {356} {3467} {34567}
%e {6} {46} {367} {3567}
%e {7} {47} {456} {4567}
%e {56} {457}
%e {57} {467}
%e {67} {567}
%t Table[Length[Select[Subsets[Range[n]],SubsetQ[#,Select[Plus@@@Tuples[#,2],#<=n&]]&]],{n,0,10}]
%Y Cf. A007865, A050291, A051026, A054519, A085489, A093971, A103580, A120641, A151897, A326020, A326023, A326076, A326080.
%K nonn
%O 0,2
%A _Gus Wiseman_, Jun 05 2019
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