A328431 Number of inversion sequences of length n avoiding the consecutive patterns 010, 021, 120, and 210.

1, 1, 2, 5, 15, 53, 214, 960, 4701, 24873, 141147, 853641, 5472642, 37024569, 263342224, 1962835806, 15288074104, 124120865849, 1048092680689, 9186689045482, 83435365244510, 783923558286071, 7608398620990535, 76177574145052258, 785853360840424425

Offset

0,3

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 010, 021, 120, and 210.

Links

Table of n, a(n) for n=0..24.

Juan S. Auli and Sergi Elizalde, Consecutive patterns in inversion sequences II: avoiding patterns of relations, arXiv:1906.07365 [math.CO], 2019.

Example

The a(4)=15 length 4 inversion sequences avoiding the consecutive patterns 010, 021, 120, and 210 are 0000, 0110, 0001, 0011, 0111, 0002, 0012, 0112, 0022, 0122, 0003, 0013, 0113, 0023, and 0123.

Maple

# after Alois P. Heinz in A328357
b := proc(n, x, t) option remember; `if`(n = 0, 1, add(
       `if`(t and i <> x, 0, b(n - 1, i, x < i)), i = 0 .. n - 1))
     end proc:
a := n -> b(n, n, false):
seq(a(n), n = 0 .. 24);

Mathematica

b[n_, x_, t_] := b[n, x, t] = If[n == 0, 1, Sum[If[t && i != x, 0, b[n - 1, i, x < i]], {i, 0, n - 1}]];
a[n_] := b[n, n, False];
a /@ Range[0, 24] (* Jean-François Alcover, Mar 02 2020 after Alois P. Heinz in A328357 *)

Crossrefs

Cf. A328357, A328358, A328429, A328430, A328432, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Sequence in context: A006790 A007548 A360052 * A120567 A263779 A328432

Adjacent sequences: A328428 A328429 A328430 * A328432 A328433 A328434

Keyword

nonn

Author

Juan S. Auli, Oct 16 2019

Status

approved