OFFSET
0,8
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(9) = 8 partitions:
. . . . . (2111) (21111) (322) (3221) (3222)
(31111) (32111) (32211)
(211111) (311111) (42111)
(2111111) (321111)
(411111)
(2211111)
(3111111)
(21111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !LessEqual@@Total/@Split[Reverse[#]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 18 2022
STATUS
approved