

A371791


Number of biquanimous subsets of {1..n}. Sets with a subset having the same sum as the complement.


25



1, 1, 1, 2, 4, 8, 18, 38, 82, 175, 373, 787, 1651, 3439, 7126, 14667
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OFFSET

0,4


COMMENTS

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.


LINKS



EXAMPLE

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}


MATHEMATICA

biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[Subsets[Range[n]], biqQ]], {n, 0, 15}]


CROSSREFS

A371781 lists numbers with biquanimous prime signature, complement A371782.
A371783 counts kquanimous partitions.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



