A328507 Number of inversion sequences of length n avoiding the consecutive pattern 101.

1, 1, 2, 6, 23, 109, 619, 4113, 31352, 269841, 2589026, 27404677, 317265161, 3988181568, 54099618419, 787705115000, 12253696410675, 202831037178017, 3559585021719875, 66018657264425355, 1290284788431977106, 26505045303122642171, 570918508059059670322

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Juan S. Auli, Pattern Avoidance in Inversion Sequences, Ph. D. thesis, Dartmouth College, ProQuest Dissertations Publishing (2020), 27964164.

Juan S. Auli, Sergi Elizalde, Consecutive Patterns in Inversion Sequences, arXiv:1904.02694 [math.CO], 2019. See Table 4.

Formula

a(n) ~ n! * c / sqrt(n), where c = 2.48988835987151440021135203237... - Vaclav Kotesovec, Oct 19 2019

Maple

b:= proc(n, j, t) option remember; `if`(n=0, 1, add(
      `if`(i<=j or i<>t, b(n-1, i, j), 0), i=1..n))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 18 2019

Mathematica

b[n_, j_, t_] := b[n, j, t] = If[n == 0, 1, Sum[If[i <= j || i != t, b[n-1, i, j], 0], {i, 1, n}]];
a[n_] := b[n, 0, 0];
a /@ Range[0, 25] (* Jean-François Alcover, Mar 19 2020, after Alois P. Heinz *)

Crossrefs

Cf. A049774, A052169, A071075, A200404.

Sequence in context: A289681 A002136 A328441 * A208733 A264899 A224786

Adjacent sequences: A328504 A328505 A328506 * A328508 A328509 A328510

Keyword

nonn

Author

Vaclav Kotesovec and Juan S. Auli, Oct 17 2019

Status

approved