OFFSET
0,5
COMMENTS
An anti-run is a sequence with no adjacent equal terms. The maxima of maximal anti-runs in a sequence are obtained by splitting it into maximal anti-run subsequences and taking the greatest term of each.
EXAMPLE
The partition y = (3,2,2,1) has maximal ant-runs ((3,2),(2,1)), with maxima (3,2), so y is not counted under a(8).
The a(2) = 1 through a(8) = 12 partitions:
(11) (111) (22) (221) (33) (331) (44)
(1111) (2111) (222) (2221) (332)
(11111) (2211) (4111) (2222)
(3111) (22111) (3311)
(21111) (31111) (5111)
(111111) (211111) (22211)
(1111111) (32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Max/@Split[#, UnsameQ]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 17 2024
STATUS
approved