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A332727
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Number of compositions of n whose run-lengths are not unimodal.
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12
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0, 0, 0, 0, 0, 0, 1, 3, 8, 28, 74, 188, 468, 1120, 2596, 5944, 13324, 29437, 64288, 138929, 297442, 632074, 1333897, 2798352, 5840164, 12132638, 25102232, 51750419, 106346704, 217921161, 445424102, 908376235, 1848753273, 3755839591, 7617835520, 15428584567, 31207263000
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OFFSET
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0,8
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COMMENTS
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A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
A composition of n is a finite sequence of positive integers summing to n.
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LINKS
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FORMULA
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EXAMPLE
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The a(6) = 1 through a(8) = 8 compositions:
(11211) (11311) (11411)
(111211) (111311)
(112111) (112112)
(113111)
(211211)
(1111211)
(1112111)
(1121111)
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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[Join@@Permutations/@IntegerPartitions[n], !unimodQ[Length/@Split[#]]&]], {n, 0, 10}]
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CROSSREFS
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Looking at the composition itself (not its run-lengths) gives A115981.
The case of partitions is A332281, with complement counted by A332280.
The complement is counted by A332726.
Non-unimodal normal sequences are A328509.
Compositions with normal run-lengths are A329766.
Numbers whose prime signature is not unimodal are A332282.
Partitions whose 0-appended first differences are unimodal are A332283, with complement A332284, with Heinz numbers A332287.
Compositions whose negation is not unimodal are A332669.
Compositions whose run-lengths are weakly increasing are A332836.
Cf. A007052, A072706, A100883, A181819, A227038, A328509, A329744, A329746, A332578, A332638, A332639, A332670, A332741, A332833.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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