OFFSET
0,10
EXAMPLE
The a(n) partitions for selected n:
n = 3 9 15 18 19 20 21
-----------------------------------------------------------
21 4221 622221 633222 633322 644321 643332
4311 632211 643221 643321 653321 654321
642111 643311 644221 654221 665211
651111 644211 644311 654311 82222221
653211 653221 82222211 83222211
663111 653311 84221111 84222111
654211 86111111 85221111
664111 86211111
87111111
For example, the partition (6,6,3,1,1,1) has conjugate (6,3,3,2,2,2), and has 2 even, 4 odd, 4 even conjugate, and 2 odd conjugate parts, so is counted under a(18).
MATHEMATICA
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Length[Select[IntegerPartitions[n], Count[#, _?EvenQ]==Count[conj[#], _?OddQ]&&Count[#, _?OddQ]==Count[conj[#], _?EvenQ]&]], {n, 0, 30}]
CROSSREFS
These partitions are ranked by A351980.
There are four statistics:
There are four other pairings of statistics:
- A045931: # of even parts = # of odd parts:
- conjugate also A045931
- ordered A098123
- strict A239241
- ranked by A325698
- conjugate ranked by A350848
There are two other double-pairings of statistics:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2022
STATUS
approved