login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A328358 Number of inversion sequences of length n avoiding the consecutive patterns 012, 021, 010, 120. 21
1, 1, 2, 4, 10, 30, 100, 376, 1566, 7094, 34751, 182841, 1026167, 6112799, 38489481, 255204077, 1776046697, 12936265145, 98368170749, 779127467795, 6414876317675, 54802126603135, 484967246285755, 4438877330941077, 41963817964950737, 409224941931240185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A length n inversion sequence e_1e_2...e_n is a sequence of integers such that 0 <= e_i < i. The term a(n) counts the inversion sequences of length n with no entries e_i, e_{i+1}, e_{i+2} such that e_i < e_{i+1} != e_{i+2}. This is the same as the set of inversion sequences of length n avoiding the consecutive patterns 012, 021, 010, 120.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..578

Juan S. Auli and Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019.

EXAMPLE

The length 4 inversion sequences avoiding the consecutive patterns 012, 021, 010, 120 are 0000, 0110, 0001, 0011, 0111, 0002, 0112, 0022, 0003, 0113.

MAPLE

b:= proc(n, x, t, c) option remember; `if`(n=0, 1, add(`if`(i<x

      and t and c=0, 0, b(n-1, i, i<>x, max(0, c-1))), i=1..n))

    end:

a:= n-> b(n, 0, false, 2):

seq(a(n), n=0..25);  # Alois P. Heinz, Oct 14 2019

MATHEMATICA

b[n_, x_, t_, c_] := b[n, x, t, c] = If[n == 0, 1, Sum[If[i < x && t && c == 0, 0, b[n - 1, i, i != x, Max[0, c - 1]]], {i, 1, n}]];

a[n_] := b[n, 0, False, 2];

a /@ Range[0, 25] (* Jean-Fran├žois Alcover, Mar 01 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A328357, A328429, A328430, A328431, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Sequence in context: A003289 A087161 A337488 * A007558 A094957 A000733

Adjacent sequences:  A328355 A328356 A328357 * A328359 A328360 A328361

KEYWORD

nonn

AUTHOR

Juan S. Auli, Oct 13 2019

EXTENSIONS

a(11)-a(25) from Alois P. Heinz, Oct 14 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 19:16 EDT 2021. Contains 348155 sequences. (Running on oeis4.)