OFFSET
1,12
COMMENTS
Also strict partitions satisfying (maximum) = 2*(mean).
These are strict partitions where both the diagram and its complement (see example) have size n.
EXAMPLE
The a(n) strict partitions for selected n (A..E = 10..14):
n=9: n=12: n=14: n=15: n=16: n=18: n=20: n=21: n=22:
--------------------------------------------------------------
621 831 7421 A32 8431 C42 A532 E43 B542
6321 A41 8521 C51 A541 E52 B632
9432 A631 E61 B641
9531 A721 B731
9621 85421 B821
86321
The a(20) = 6 strict partitions are: (10,7,2,1), (10,6,3,1), (10,5,4,1), (10,5,3,2), (8,6,3,2,1), (8,5,4,2,1).
The strict partition y = (8,5,4,2,1) has diagram:
o o o o o o o o
o o o o o . . .
o o o o . . . .
o o . . . . . .
o . . . . . . .
Since the partition and its complement (shown in dots) have the same size, y is counted under a(20).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Length[#]*Max@@#==2n&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2023
STATUS
approved