A279544 Number of length n inversion sequences avoiding the patterns 000, 010, 100, 110, 120, and 210.

1, 1, 2, 4, 10, 26, 73, 214, 651, 2040, 6549, 21453, 71485, 241702, 827603, 2865087, 10014927, 35307628, 125427569, 448616693, 1614432373, 5842129120, 21247505098, 77631329535, 284832049361, 1049092809734, 3877749157355, 14380314221305, 53490244751332

Offset: 0

Author

Megan A. Martinez, Dec 14 2016

Keywords

• nonn

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 000, 010, 100, 110, 120, and 210.

Examples

			For n=3, the inversion sequences are 001, 002, 011, 012.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..600
• Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.

Crossrefs

Cf. A000085, A263777, A263778, A263779, A263780.

Programs

Maple

b:= proc(n, i, m) option remember; `if`(i=0, 1, add(
      b(n-min(m, j), i-1, abs(m-j)), j=1..n-i+1))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..30);  # Alois P. Heinz, Dec 15 2016

Mathematica

b[n_, i_, m_] := b[n, i, m] = If[i == 0, 1, Sum[b[n - Min[m, j], i - 1, Abs[m - j]], {j, 1, n - i + 1}]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 10 2017, after Alois P. Heinz *)

Formula

a(n) ~ c * 4^n / n^(3/2), where c = 0.0549097036253448014962069269284638611865763295943683310517... - Vaclav Kotesovec, Oct 07 2021

Extensions

a(10)-a(28) from Alois P. Heinz, Dec 14 2016

Name and description corrected by Nicholas R. Beaton, May 02 2024