OFFSET
0,3
COMMENTS
LINKS
MathWorld, Unimodal Sequence
EXAMPLE
The only partition not counted under a(14) = 134 is (4,3,3,2,1,1), whose run-lengths (1,2,1,2) are neither unimodal nor is their negation.
MATHEMATICA
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]]
Table[Length[Select[IntegerPartitions[n], unimodQ[Length/@Split[#]]||unimodQ[-Length/@Split[#]]&]], {n, 0, 30}]
CROSSREFS
Looking only at the original run-lengths gives A332281.
Looking only at the negated run-lengths gives A332639.
The complement is counted by A332640.
The Heinz numbers of partitions not in this class are A332643.
Unimodal compositions are A001523.
Partitions with unimodal run-lengths are A332280.
Compositions whose negation is unimodal are A332578.
Partitions whose negated run-lengths are unimodal are A332638.
Run-lengths are neither weakly increasing nor weakly decreasing: A332641.
Run-lengths and negated run-lengths are both unimodal: A332745.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 27 2020
STATUS
approved