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

Author

Vaclav Kotesovec and Juan S. Auli, Oct 17 2019

Keywords

• nonn

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.

Crossrefs

Cf. A049774, A052169, A071075, A200404.

Programs

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 *)

Formula

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