A328500 Number of inversion sequences of length n avoiding the consecutive pattern 102.

1, 1, 2, 6, 22, 96, 492, 2902, 19350, 143918, 1181540, 10614698, 103589738, 1091367634, 12346368424, 149276823258, 1921099070062, 26220186000950, 378308908684300, 5753387612678314, 91988260677198002, 1542570178562361018, 27072325866355742048

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 3.

Crossrefs

Cf. A049774, 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 01 2020, after Alois P. Heinz *)

Formula

a(n) ~ n! * c * d^n * n^alfa, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))), alfa = 0.294868853646259565..., c = 2.22826071050847602... - Vaclav Kotesovec, Oct 19 2019