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A371791
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Number of biquanimous subsets of {1..n}. Sets with a subset having the same sum as the complement.
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25
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1, 1, 1, 2, 4, 8, 18, 38, 82, 175, 373, 787, 1651, 3439, 7126, 14667
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OFFSET
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0,4
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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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For S = {1,3,4,6} we have {{1,6},{3,4}}, so S is counted under a(6).
The a(0) = 1 through a(6) = 18 subsets:
{} {} {} {} {} {} {}
{1,2,3} {1,2,3} {1,2,3} {1,2,3}
{1,3,4} {1,3,4} {1,3,4}
{1,2,3,4} {1,4,5} {1,4,5}
{2,3,5} {1,5,6}
{1,2,3,4} {2,3,5}
{1,2,4,5} {2,4,6}
{2,3,4,5} {1,2,3,4}
{1,2,3,6}
{1,2,4,5}
{1,2,5,6}
{1,3,4,6}
{2,3,4,5}
{2,3,5,6}
{3,4,5,6}
{1,2,3,4,6}
{1,2,4,5,6}
{2,3,4,5,6}
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MATHEMATICA
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biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[Subsets[Range[n]], biqQ]], {n, 0, 15}]
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CROSSREFS
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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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