OFFSET
1,6
COMMENTS
Also partitions such that (maximum) >= 2*(mean).
These are partitions whose complement (see example) has size >= n.
EXAMPLE
The a(6) = 2 through a(10) = 15 partitions:
(411) (511) (611) (621) (721)
(3111) (4111) (4211) (711) (811)
(31111) (5111) (5211) (5221)
(41111) (6111) (5311)
(311111) (42111) (6211)
(51111) (7111)
(321111) (42211)
(411111) (43111)
(3111111) (52111)
(61111)
(421111)
(511111)
(3211111)
(4111111)
(31111111)
The partition y = (4,2,1,1) has length 4 and maximum 4, and 4*4 >= 2*8, so y is counted under a(8).
The partition y = (3,2,1,1) has length 4 and maximum 3, and 4*3 is not >= 2*7, so y is not counted under a(7).
The partition y = (3,2,1,1) has diagram:
o o o
o o .
o . .
o . .
with complement (shown in dots) of size 5, and 5 is not >= 7, so y is not counted under a(7).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]*Max@@#>=2n&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 29 2023
STATUS
approved