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A325096
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Number of maximal subsets of {1...n} with no binary carries.
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17
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1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 12, 13, 14, 15, 15, 20, 25, 27, 32, 34, 36, 37, 42, 44, 46, 47, 49, 50, 51, 52, 52, 67, 82, 87, 102, 107, 112, 114, 129, 134, 139, 141, 146, 148, 150, 151, 166, 171, 176, 178, 183, 185, 187, 188, 193, 195, 197, 198, 200, 201
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OFFSET
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0,4
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COMMENTS
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A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(9) = 7 maximal subsets:
{1} {12} {3} {34} {25} {16} {7} {78} {69}
{12} {124} {34} {25} {16} {168} {78}
{124} {34} {25} {258} {168}
{124} {34} {348} {249}
{124} {1248} {258}
{348}
{1248}
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MATHEMATICA
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binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];
Table[Length[maxim[Select[Subsets[Range[n]], stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]]], {n, 0, 10}]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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