OFFSET
0,10
EXAMPLE
The a(n) partitions for selected n (A..C = 10..12):
n = 3 9 15 18 20
----------------------------------------------------------
(21) (63) (A5) (8433) (8543)
(222111) (632211) (8532) (8741)
(642111) (8631) (C611)
(2222211111) (43322211) (43332221)
(44322111) (44432111)
(44421111) (84221111)
(422222111111)
MATHEMATICA
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}]
CROSSREFS
These partitions are ranked by A350946.
The strict case is A352128.
There are four statistics:
There are four additional pairings of statistics:
There are two additional double-pairings of statistics:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 14 2022
STATUS
approved