OFFSET
1,2
COMMENTS
Also partitions such that (maximum) < 2*(mean).
EXAMPLE
The a(1) = 1 through a(7) = 12 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (321) (331)
(11111) (2211) (421)
(21111) (2221)
(111111) (3211)
(22111)
(211111)
(1111111)
For example, the partition y = (3,2,1,1) has length 4 and maximum 3, and 4*3 < 2*7, so y is counted under a(7).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]*Max@@#<2n&]], {n, 30}]
CROSSREFS
For length instead of mean we have A237754.
For median instead of mean we have A361858.
The complement is counted by A361906.
Reversing the inequality gives A361907.
A051293 counts subsets with integer mean.
A067538 counts partitions with integer mean.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2023
STATUS
approved