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A328509 Number of non-unimodal sequences of length n covering an initial interval of positive integers. 45
0, 0, 0, 3, 41, 425, 4287, 45941, 541219, 7071501 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A sequence of 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..9.

MathWorld, Unimodal Sequence

EXAMPLE

The a(3) = 3 sequences are (2,1,2), (2,1,3), (3,1,2).

The a(4) = 41 sequences:

(1212) (2113) (2134) (2413) (3142) (3412)

(1213) (2121) (2143) (3112) (3212) (4123)

(1312) (2122) (2212) (3121) (3213) (4132)

(1323) (2123) (2213) (3122) (3214) (4213)

(1324) (2131) (2312) (3123) (3231) (4231)

(1423) (2132) (2313) (3124) (3241) (4312)

(2112) (2133) (2314) (3132) (3312)

MATHEMATICA

allnorm[n_]:=If[n<=0, {{}}, Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]];

unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];

Table[Length[Select[Union@@Permutations/@allnorm[n], !unimodQ[#]&]], {n, 0, 5}]

CROSSREFS

Not requiring non-unimodality gives A000670.

The complement appears to be counted by A007052.

The case where the negation is not unimodal either is A332873.

Unimodal compositions are A001523.

Non-unimodal permutations are A059204.

Non-unimodal compositions are A115981.

Unimodal compositions covering an initial interval are A227038.

Numbers whose unsorted prime signature is not unimodal are A332282.

Covering partitions with unimodal run-lengths are A332577.

Non-unimodal compositions covering an initial interval are A332743.

Cf. A060223, A255906, A332281, A332284, A332639, A332672, A332834, A332870.

Sequence in context: A322244 A181226 A159249 * A087544 A305667 A213378

Adjacent sequences: A328506 A328507 A328508 * A328510 A328511 A328512

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Feb 19 2020

EXTENSIONS

a(9) from Robert Price, Jun 19 2021

STATUS

approved

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Last modified December 7 19:19 EST 2022. Contains 358669 sequences. (Running on oeis4.)