OFFSET
0,3
EXAMPLE
The a(1) = 1 through a(8) = 13 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (221) (33) (322) (44)
(211) (311) (222) (331) (332)
(1111) (2111) (411) (511) (422)
(11111) (3111) (2221) (611)
(21111) (4111) (2222)
(111111) (22111) (5111)
(31111) (22211)
(211111) (41111)
(1111111) (221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Or[Less@@Length/@Split[#], Greater@@Length/@Split[#]]&]], {n, 0, 30}]
CROSSREFS
The non-strict version is A332745.
The generalization to compositions is A333191.
Partitions with distinct run-lengths are A098859.
Partitions with strictly increasing run-lengths are A100471.
Partitions with strictly decreasing run-lengths are A100881.
Partitions with weakly decreasing run-lengths are A100882.
Partitions with weakly increasing run-lengths are A100883.
Partitions with unimodal run-lengths are A332280.
Partitions whose run-lengths are not increasing nor decreasing are A332641.
Compositions whose run-lengths are unimodal or co-unimodal are A332746.
Compositions that are neither increasing nor decreasing are A332834.
Strictly increasing or strictly decreasing compositions are A333147.
Compositions with strictly increasing run-lengths are A333192.
Numbers with strictly increasing prime multiplicities are A334965.
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2020
STATUS
approved