A328358 Number of inversion sequences of length n avoiding the consecutive patterns 012, 021, 010, 120.

1, 1, 2, 4, 10, 30, 100, 376, 1566, 7094, 34751, 182841, 1026167, 6112799, 38489481, 255204077, 1776046697, 12936265145, 98368170749, 779127467795, 6414876317675, 54802126603135, 484967246285755, 4438877330941077, 41963817964950737, 409224941931240185

Offset: 0

Author

Juan S. Auli, Oct 13 2019

Keywords

• nonn

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers such that 0 <= e_i < i. The term a(n) counts the inversion sequences of length n with no entries e_i, e_{i+1}, e_{i+2} such that e_i < e_{i+1} != e_{i+2}. This is the same as the set of inversion sequences of length n avoiding the consecutive patterns 012, 021, 010, 120.

Examples

			The length 4 inversion sequences avoiding the consecutive patterns 012, 021, 010, 120 are 0000, 0110, 0001, 0011, 0111, 0002, 0112, 0022, 0003, 0113.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..578
• Juan S. Auli and Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019.

Crossrefs

Cf. A328357, A328429, A328430, A328431, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Programs

Maple

b:= proc(n, x, t, c) option remember; `if`(n=0, 1, add(`if`(ix, max(0, c-1))), i=1..n))
    end:
a:= n-> b(n, 0, false, 2):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 14 2019

Mathematica

b[n_, x_, t_, c_] := b[n, x, t, c] = If[n == 0, 1, Sum[If[i < x && t && c == 0, 0, b[n - 1, i, i != x, Max[0, c - 1]]], {i, 1, n}]];
a[n_] := b[n, 0, False, 2];
a /@ Range[0, 25] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)

Extensions

a(11)-a(25) from Alois P. Heinz, Oct 14 2019