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A370644
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Number of minimal subsets of {2..n} such that it is not possible to choose a different binary index of each element.
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6
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0, 0, 0, 0, 0, 1, 4, 13, 13, 26, 56, 126, 243, 471, 812, 1438
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OFFSET
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0,7
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COMMENTS
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A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
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LINKS
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EXAMPLE
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The a(0) = 0 through a(7) = 13 subsets:
. . . . . {2,3,4,5} {2,4,6} {2,4,6}
{2,3,4,5} {2,3,4,5}
{2,3,5,6} {2,3,4,7}
{3,4,5,6} {2,3,5,6}
{2,3,5,7}
{2,3,6,7}
{2,4,5,7}
{2,5,6,7}
{3,4,5,6}
{3,4,5,7}
{3,4,6,7}
{3,5,6,7}
{4,5,6,7}
The a(0) = 0 through a(7) = 13 set-systems:
. . . . . {2}{12}{3}{13} {2}{3}{23} {2}{3}{23}
{2}{12}{3}{13} {2}{12}{3}{13}
{12}{3}{13}{23} {12}{3}{13}{23}
{2}{12}{13}{23} {2}{12}{13}{23}
{2}{12}{3}{123}
{2}{3}{13}{123}
{12}{3}{13}{123}
{12}{3}{23}{123}
{2}{12}{13}{123}
{2}{12}{23}{123}
{2}{13}{23}{123}
{3}{13}{23}{123}
{12}{13}{23}{123}
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
fasmin[y_]:=Complement[y, Union@@Table[Union[s, #]& /@ Rest[Subsets[Complement[Union@@y, s]]], {s, y}]];
Table[Length[fasmin[Select[Subsets[Range[2, n]], Select[Tuples[bpe/@#], UnsameQ@@#&]=={}&]]], {n, 0, 10}]
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CROSSREFS
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This is the minimal case of A370643.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A370585 counts maximal choosable sets.
Cf. A072639, A140637, A326031, A355529, A367905, A368109, A370589, A370591, A370636, A370639, A370640.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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