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A371795
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Number of non-biquanimous integer partitions of n.
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27
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0, 1, 1, 3, 2, 7, 5, 15, 8, 30, 17, 56, 24, 101, 46, 176, 64, 297, 107, 490, 147, 792, 242, 1255, 302, 1958, 488, 3010, 629, 4565, 922
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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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The a(1) = 1 through a(8) = 8 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(21) (31) (32) (42) (43) (53)
(111) (41) (51) (52) (62)
(221) (222) (61) (71)
(311) (411) (322) (332)
(2111) (331) (521)
(11111) (421) (611)
(511) (5111)
(2221)
(3211)
(4111)
(22111)
(31111)
(211111)
(1111111)
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MATHEMATICA
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biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[IntegerPartitions[n], Not@*biqQ]], {n, 0, 15}]
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CROSSREFS
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These partitions have ranks A371731.
A371781 lists numbers with biquanimous prime signature, complement A371782.
A371783 counts k-quanimous partitions.
Cf. A035470, A064914, A305551, A336137, A365543, A365661, A365663, A366320, A365925, A367094, A371788.
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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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