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A351978
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Number of integer partitions of n for which the number of even parts, the number of odd parts, the number of even conjugate parts, and the number of odd conjugate parts are all equal.
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15
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1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 6, 1, 3, 1, 8, 5, 3, 5, 7, 14, 2, 13, 9, 28, 5, 22, 26, 44, 17, 30, 60, 59, 42, 41, 120, 84, 84, 66, 204, 143, 144, 131, 325, 268, 226, 261, 486, 498, 344, 488, 739, 874
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OFFSET
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0,13
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LINKS
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EXAMPLE
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The a(n) partitions for selected n (A = 10):
n = 3 12 19 21 23 24 27
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21 4332 633322 643332 644333 84332211 655443
4431 643321 654321 654332 84441111 655542
644311 665211 654431 85322211 665541
653221 655322 86322111 666333
654211 655421 86421111 666531
664111 664331 A522221111
665321 A622211111
666311
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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[#, _?EvenQ]==Count[#, _?OddQ]==Count[conj[#], _?EvenQ]==Count[conj[#], _?OddQ]&]], {n, 0, 30}]
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CROSSREFS
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The strict case appears to be the indicator function for A014105.
These partitions are ranked by A350947.
There are four statistics:
There are six pairings of statistics:
- A045931: # of even parts = # of odd parts:
There are three double-pairings of statistics:
A103919 and A116482 count partitions by sum and number of odd/even parts.
A195017 = # of even parts - # of odd parts.
Cf. A000070, A122111, A130780, A171966, A236559, A236914, A350849, A350941, A350942, A350950, A350951.
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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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