OFFSET
0,6
COMMENTS
The Heinz numbers of these partitions are given by A325241.
For example, the partition (44111) has two multiplicities (2 and 3) which differ by 1, so is counted under a(11).
EXAMPLE
The a(4) = 1 through a(11) = 18 partitions:
(211) (221) (411) (322) (332) (441) (433) (443)
(311) (331) (422) (522) (442) (533)
(511) (611) (711) (622) (551)
(3211) (3221) (3321) (811) (722)
(22111) (4211) (4221) (5221) (911)
(22211) (4311) (5311) (4322)
(5211) (6211) (4331)
(32211) (33211) (4421)
(33111) (42211) (5411)
(2221111) (6221)
(6311)
(7211)
(33221)
(33311)
(43211)
(44111)
(52211)
(2222111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Max@@Length/@Split[#]-Min@@Length/@Split[#]==1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 18 2019
STATUS
approved