login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 17:27 EDT 2022. Contains 357106 sequences. (Running on oeis4.)