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 A326083 Number of subsets of {1..n} containing all of their pairwise sums <= n. 92
 1, 2, 3, 5, 7, 12, 16, 27, 37, 58, 80, 131, 171, 277, 380, 580, 785, 1250, 1655, 2616, 3516, 5344, 7257, 11353, 14931, 23204, 31379, 47511, 63778, 98681, 130503, 201357, 270038, 407429, 548090, 840171, 1110429, 1701872, 2284325, 3440337, 4601656 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). From Gus Wiseman, Jul 08 2019: (Start) 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: {} {} {} {} {} {} {} {1} {1} {1} {1} {1} {1} {2} {2} {2} {2} {2} {3} {3} {3} {3} {2,3} {4} {4} {4} {2,3} {5} {5} {3,4} {2,3} {6} {2,5} {2,3} {3,4} {2,5} {3,5} {3,4} {4,5} {3,5} {3,4,5} {4,5} {4,6} {5,6} {3,4,5} {4,5,6} (End) LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..100 FORMULA For n > 0, a(n) = A103580(n) + 1. EXAMPLE The a(0) = 1 through a(6) = 16 subsets: {} {} {} {} {} {} {} {1} {2} {2} {3} {3} {4} {1,2} {3} {4} {4} {5} {2,3} {2,4} {5} {6} {1,2,3} {3,4} {2,4} {3,6} {2,3,4} {3,4} {4,5} {1,2,3,4} {3,5} {4,6} {4,5} {5,6} {2,4,5} {2,4,6} {3,4,5} {3,4,6} {2,3,4,5} {3,5,6} {1,2,3,4,5} {4,5,6} {2,4,5,6} {3,4,5,6} {2,3,4,5,6} {1,2,3,4,5,6} The a(7) = 27 subsets: {} {4} {36} {246} {2467} {24567} {234567} {1234567} {5} {45} {356} {3467} {34567} {6} {46} {367} {3567} {7} {47} {456} {4567} {56} {457} {57} {467} {67} {567} MATHEMATICA Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Plus@@@Tuples[#, 2], #<=n&]]&]], {n, 0, 10}] CROSSREFS Cf. A007865, A050291, A051026, A054519, A085489, A093971, A103580, A120641, A151897, A326020, A326023, A326076, A326080. Sequence in context: A319635 A179822 A319769 * A027959 A060730 A308928 Adjacent sequences: A326080 A326081 A326082 * A326084 A326085 A326086 KEYWORD nonn AUTHOR Gus Wiseman, Jun 05 2019 STATUS approved

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Last modified April 21 12:56 EDT 2024. Contains 371870 sequences. (Running on oeis4.)