OFFSET
0,3
COMMENTS
Also partitions whose run-lengths and negated run-lengths are both unimodal.
EXAMPLE
The a(8) = 21 partitions are:
(8) (44) (2222)
(53) (332) (22211)
(62) (422) (32111)
(71) (431) (221111)
(521) (3311) (311111)
(611) (4211) (2111111)
(5111) (41111) (11111111)
Missing from this list is only (3221).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Or[LessEqual@@Length/@Split[#], GreaterEqual@@Length/@Split[#]]&]], {n, 0, 30}]
CROSSREFS
The complement is counted by A332641.
The Heinz numbers of partitions not in this class are A332831.
The case of run-lengths of compositions is A332835.
Only weakly decreasing is A100882.
Only weakly increasing is A100883.
Unimodal compositions are A001523.
Non-unimodal compositions are A115981.
Partitions with unimodal run-lengths are A332280.
Partitions whose negated run-lengths are unimodal are A332638.
Compositions with unimodal run-lengths are A332726.
Compositions that are neither weakly increasing nor decreasing are A332834.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 29 2020
STATUS
approved