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A371794
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Number of non-biquanimous strict integer partitions of n.
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22
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0, 1, 1, 2, 2, 3, 3, 5, 5, 8, 7, 12, 11, 18, 15, 27, 23, 38, 30, 54, 43, 76, 57, 104, 79, 142, 102, 192, 138, 256, 174, 340, 232, 448, 292, 585, 375, 760, 471, 982, 602, 1260, 741, 1610, 935, 2048, 1148, 2590, 1425, 3264, 1733, 4097, 2137, 5120, 2571, 6378
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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(11) = 12 strict partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(21) (31) (32) (42) (43) (53) (54) (64) (65)
(41) (51) (52) (62) (63) (73) (74)
(61) (71) (72) (82) (83)
(421) (521) (81) (91) (92)
(432) (631) (A1)
(531) (721) (542)
(621) (632)
(641)
(731)
(821)
(5321)
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MATHEMATICA
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biqQ[y_]:=MemberQ[Total/@Subsets[y], Total[y]/2];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!biqQ[#]&]], {n, 0, 30}]
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CROSSREFS
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A371781 lists numbers with biquanimous prime signature, complement A371782.
A371783 counts k-quanimous partitions.
Cf. A064914, A279787, A305551, A318434, A365543, A365663, A365661, A366320, A365925, A367094, A371788.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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