OFFSET
0,6
COMMENTS
The sequence of runs of a sequence consists of its maximal consecutive constant subsequences when read left-to-right. For example, the runs of (2,2,1,1,1,3,2,2) are (2,2), (1,1,1), (3), (2,2), with sums (4,3,3,4).
LINKS
Mathematics Stack Exchange, What is a sequence run? (answered 2011-12-01)
EXAMPLE
The a(0) = 0 through a(8) = 13 partitions:
. . . (21) (31) (32) (42) (43) (53)
(41) (51) (52) (62)
(221) (321) (61) (71)
(311) (411) (331) (332)
(2211) (421) (431)
(511) (521)
(2221) (611)
(3211) (3221)
(4111) (3311)
(22111) (4211)
(5111)
(22211)
(32111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !LessEqual@@Total/@Split[#]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 19 2022
STATUS
approved