OFFSET
0,13
EXAMPLE
The a(n) partitions for selected n (A = 10):
n = 3 12 19 21 23 24 27
--------------------------------------------------------------
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
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[#, _?OddQ]==Count[conj[#], _?EvenQ]==Count[conj[#], _?OddQ]&]], {n, 0, 30}]
CROSSREFS
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:
- ordered A098123
- strict A239241
- ranked by A325698
There are three double-pairings of statistics:
A195017 = # of even parts - # of odd parts.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 15 2022
STATUS
approved