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A332639 Number of integer partitions of n whose negated run-lengths are not unimodal. 33
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 10, 17, 25, 36, 51, 75, 102, 143, 192, 259, 346, 462, 599, 786, 1014, 1309, 1670, 2133, 2686, 3402, 4258, 5325, 6623, 8226, 10134, 12504, 15328, 18779, 22878, 27870, 33762, 40916, 49349, 59457, 71394, 85679, 102394 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.

LINKS

Table of n, a(n) for n=0..49.

MathWorld, Unimodal Sequence

EXAMPLE

The a(8) = 1 through a(13) = 10 partitions:

  (3221)  (4221)  (5221)   (4331)    (4332)    (5332)

                  (32221)  (6221)    (5331)    (6331)

                           (42221)   (7221)    (8221)

                           (322211)  (43221)   (43321)

                                     (52221)   (53221)

                                     (322221)  (62221)

                                     (422211)  (332221)

                                               (422221)

                                               (522211)

                                               (3222211)

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[#]]&]], {n, 0, 30}]

CROSSREFS

The version for normal sequences is A328509.

The non-negated complement is A332280.

The non-negated version is A332281.

The complement is counted by A332638.

The case that is not unimodal either is A332640.

The Heinz numbers of these partitions are A332642.

The generalization to run-lengths of compositions is A332727.

Unimodal compositions are A001523.

Non-unimodal permutations are A059204.

Non-unimodal compositions are A115981.

Compositions whose negation is not unimodal are A332669.

Cf. A007052, A025065, A100883, A181819, A332282, A332578, A332579, A332641, A332670, A332671, A332726, A332742, A332744.

Sequence in context: A062365 A049630 A032705 * A281168 A274352 A343328

Adjacent sequences:  A332636 A332637 A332638 * A332640 A332641 A332642

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 25 2020

STATUS

approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)