OFFSET
0,7
COMMENTS
None of these partitions is strict.
Also the number of integer partitions of n which, after appending 0, have first differences of median 0.
EXAMPLE
The a(3) = 1 through a(9) = 10 partitions:
(111) (1111) (11111) (222) (22111) (2222) (333)
(21111) (31111) (22211) (22221)
(111111) (211111) (41111) (33111)
(1111111) (221111) (51111)
(311111) (222111)
(2111111) (411111)
(11111111) (2211111)
(3111111)
(21111111)
(111111111)
For example, the partition y = (4,4,3,1,1,1,1) has 0-appended differences (0,1,2,0,0,0,0), with median 0, so y is counted under a(15).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]>2*Length[Union[#]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 20 2023
STATUS
approved