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A370640
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Number of maximal subsets of {1..n} such that it is possible to choose a different binary index of each element.
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12
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1, 1, 1, 3, 3, 8, 17, 32, 32, 77, 144, 242, 383, 580, 843, 1201, 1201, 2694, 4614, 7096, 10219, 14186, 19070, 25207, 32791, 42160
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OFFSET
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0,4
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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.
Also choices of A029837(n) elements of {1..n} such that it is possible to choose a different binary index of each.
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LINKS
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EXAMPLE
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The a(0) = 1 through a(6) = 17 subsets:
{} {1} {1,2} {1,2} {1,2,4} {1,2,4} {1,2,4}
{1,3} {1,3,4} {1,2,5} {1,2,5}
{2,3} {2,3,4} {1,3,4} {1,2,6}
{1,3,5} {1,3,4}
{2,3,4} {1,3,5}
{2,3,5} {1,3,6}
{2,4,5} {1,4,6}
{3,4,5} {1,5,6}
{2,3,4}
{2,3,5}
{2,3,6}
{2,4,5}
{2,5,6}
{3,4,5}
{3,4,6}
{3,5,6}
{4,5,6}
The a(0) = 1 through a(6) = 17 set-systems:
{1} {1}{2} {1}{2} {1}{2}{3} {1}{2}{3} {1}{2}{3}
{1}{12} {1}{12}{3} {1}{12}{3} {1}{12}{3}
{2}{12} {2}{12}{3} {1}{2}{13} {1}{2}{13}
{2}{12}{3} {1}{2}{23}
{2}{3}{13} {1}{3}{23}
{1}{12}{13} {2}{12}{3}
{12}{3}{13} {2}{3}{13}
{2}{12}{13} {1}{12}{13}
{1}{12}{23}
{1}{13}{23}
{12}{3}{13}
{12}{3}{23}
{2}{12}{13}
{2}{12}{23}
{2}{13}{23}
{3}{13}{23}
{12}{13}{23}
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MATHEMATICA
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bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Subsets[Range[n], {IntegerLength[n, 2]}], Select[Tuples[bpe/@#], UnsameQ@@#&]!={}&]], {n, 0, 10}]
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CROSSREFS
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The case of a unique choice is A370638.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A307984 counts Q-bases of logarithms of positive integers.
A355741 counts choices of a prime factor of each prime index.
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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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