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A361864
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Number of set partitions of {1..n} whose block-medians have integer median.
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8
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1, 0, 3, 6, 30, 96, 461, 2000, 10727, 57092, 342348
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OFFSET
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1,3
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COMMENTS
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The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
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LINKS
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EXAMPLE
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The a(1) = 1 through a(4) = 6 set partitions:
{{1}} . {{123}} {{1}{234}}
{{13}{2}} {{123}{4}}
{{1}{2}{3}} {{1}{2}{34}}
{{12}{3}{4}}
{{1}{24}{3}}
{{13}{2}{4}}
The set partition {{1,2},{3},{4}} has block-medians {3/2,3,4}, with median 3, so is counted under a(4).
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MATHEMATICA
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sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]& /@ sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[Range[n]], IntegerQ[Median[Median/@#]]&]], {n, 6}]
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CROSSREFS
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For mean instead of median we have A361865.
A308037 counts set partitions with integer average block-size.
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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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