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A351977
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Number of integer partitions of n with as many even parts as odd parts and as many even conjugate parts as odd conjugate parts.
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15
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1, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 0, 2, 4, 2, 1, 6, 6, 7, 9, 11, 10, 13, 17, 17, 21, 28, 36, 35, 41, 58, 71, 72, 90, 106, 121, 142, 178, 191, 216, 269, 320, 344, 400, 486, 564, 633, 734, 867, 991, 1130, 1312, 1509, 1702, 1978, 2288, 2582, 2917, 3404
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OFFSET
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0,10
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LINKS
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EXAMPLE
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The a(n) partitions for selected n (A..C = 10..12):
n = 3 9 15 18 20
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(21) (63) (A5) (8433) (8543)
(222111) (632211) (8532) (8741)
(642111) (8631) (C611)
(2222211111) (43322211) (43332221)
(44322111) (44432111)
(44421111) (84221111)
(422222111111)
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MATHEMATICA
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conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[IntegerPartitions[n], Count[#, _?OddQ]==Count[#, _?EvenQ]&&Count[conj[#], _?OddQ]==Count[conj[#], _?EvenQ]&]], {n, 0, 30}]
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CROSSREFS
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These partitions are ranked by A350946.
There are four statistics:
There are four additional pairings of statistics:
There are two additional double-pairings of statistics:
Cf. A000041, A000070, A088218, A098123, A130780, A171966, A195017, A236559, A236914, A241638, A350849.
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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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