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A332638
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Number of integer partitions of n whose negated run-lengths are unimodal.
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28
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1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 52, 70, 91, 118, 151, 195, 246, 310, 388, 484, 600, 743, 909, 1113, 1359, 1650, 1996, 2409, 2895, 3471, 4156, 4947, 5885, 6985, 8260, 9751, 11503, 13511, 15857, 18559, 21705, 25304, 29499, 34259, 39785, 46101, 53360, 61594
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OFFSET
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0,3
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COMMENTS
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A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
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LINKS
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EXAMPLE
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The a(8) = 21 partitions:
(8) (44) (2222)
(53) (332) (22211)
(62) (422) (32111)
(71) (431) (221111)
(521) (3311) (311111)
(611) (4211) (2111111)
(5111) (41111) (11111111)
Missing from this list is only (3221).
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MATHEMATICA
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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[#]]&]], {n, 0, 30}]
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CROSSREFS
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The non-negated version is A332280.
The complement is counted by A332639.
The Heinz numbers of partitions not in this class are A332642.
The case of 0-appended differences (instead of run-lengths) is A332728.
Partitions whose run lengths are not unimodal are A332281.
Heinz numbers of partitions with non-unimodal run-lengths are A332282.
Compositions whose negation is unimodal are A332578.
Compositions whose run-lengths are unimodal are A332726.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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