A328504 Number of inversion sequences of length n avoiding the consecutive pattern 010.

1, 1, 2, 5, 17, 76, 417, 2701, 20199, 171329, 1624851, 17036586, 195685618, 2443572835, 32959210808, 477542545691, 7396931591165, 121976733648960, 2133460758692093, 39450254899737811, 768950119933799815, 15757352298761474101, 338663233082663363407

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 = 1.410641128930866501817126119... - 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 12 2020, after Alois P. Heinz *)

Crossrefs

Cf. A049774, A052169, A071075, A200404.

Sequence in context: A118100 A129591 A328439 * A279208 A099825 A014288

Adjacent sequences: A328501 A328502 A328503 * A328505 A328506 A328507

Keyword

nonn

Author

Vaclav Kotesovec and Juan S. Auli, Oct 17 2019

Status

approved