OFFSET
0,9
EXAMPLE
The a(n) partitions for selected n:
n = 3 8 11 12 15 16
----------------------------------------------------------
(21) (332) (4322) (4332) (4443) (4444)
(4211) (4331) (4422) (54321) (53332)
(4421) (4431) (632211) (55222)
(611111) (53211) (633111) (55411)
(621111) (642111) (633211)
(81111111) (642211)
(643111)
(7321111)
(82111111)
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[conj[#], _?OddQ]&&Count[#, _?EvenQ]==Count[conj[#], _?EvenQ]&]], {n, 0, 30}]
CROSSREFS
These partitions are ranked by A350949.
A000041 counts integer partitions.
A122111 represents partition conjugation using Heinz numbers.
A195017 = # of even parts - # of odd parts.
There are four statistics:
There are four other possible pairings of statistics:
There are two other possible double-pairings of statistics:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 14 2022
STATUS
approved