OFFSET
0,4
EXAMPLE
The a(0) = 1 through a(8) = 6 partitions (empty column indicated by dot):
() (1) . (3) (22) (5) (42) (7) (62)
(21) (41) (321) (61) (332)
(111) (311) (2211) (511) (521)
(2111) (4111) (4211)
(11111) (31111) (32111)
(211111) (221111)
(1111111)
For example, both (3,2,1,1,1) and its conjugate (5,2,1) have exactly 1 even part, so are counted under a(8).
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[#], _?EvenQ]&]], {n, 0, 30}]
CROSSREFS
Comparing product of parts to product of conjugate parts gives A325039.
A116482 counts partitions by number of even (or even conjugate) parts.
A122111 represents partition conjugation using Heinz numbers.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 14 2022
STATUS
approved