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A198085
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Number of nonempty connected, containment-free subsets of 2^[n]. Total number of clutters on all subsets of [n]. Number of connected antichains in the Boolean algebra B_n (the poset of subsets of [n] ordered by containment).
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8
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OFFSET
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1,2
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COMMENTS
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The restriction to (spanning hypergraphs = maximal antichains = clutters on [n]) is considered in A048143.
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LINKS
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Table of n, a(n) for n=1..8.
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FORMULA
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a(n) = Sum_{k=1..n} binomial(n,k) * A048143(k). - Andrew Howroyd, Feb 04 2021
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EXAMPLE
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For n=3: {{1}}, {{2}}, {{3}}, {{12}}, {{13}}, {{23}}, {{123}}, {{12}{13}}, {{12}{23}}, {{13}{23}}, {{12}{13}{23}}.
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CROSSREFS
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Cf. A048143.
Sequence in context: A275338 A068693 A036930 * A319749 A209107 A015047
Adjacent sequences: A198082 A198083 A198084 * A198086 A198087 A198088
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KEYWORD
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nonn,more
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AUTHOR
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Gus Wiseman, Oct 21 2011
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EXTENSIONS
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a(6)-a(8) from Andrew Howroyd, Feb 04 2021
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STATUS
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approved
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