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A371793
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Number of non-biquanimous subsets of {1..n} containing n.
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14
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1, 2, 3, 6, 12, 22, 44, 84, 163, 314, 610, 1184, 2308, 4505, 8843
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OFFSET
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1,2
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COMMENTS
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A finite multiset of numbers is defined to be biquanimous iff it can be partitioned into two multisets with equal sums. Biquanimous partitions are counted by A002219 and ranked by A357976.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(5) = 12 subsets:
{1} {2} {3} {4} {5}
{1,2} {1,3} {1,4} {1,5}
{2,3} {2,4} {2,5}
{3,4} {3,5}
{1,2,4} {4,5}
{2,3,4} {1,2,5}
{1,3,5}
{2,4,5}
{3,4,5}
{1,2,3,5}
{1,3,4,5}
{1,2,3,4,5}
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MATHEMATICA
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biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&!biqQ[#]&]], {n, 15}]
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CROSSREFS
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The complement is the "bi-" version of A371797, differences of A371796.
A371781 lists numbers with biquanimous prime signature, complement A371782.
A371783 counts k-quanimous partitions.
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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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