A328432 Number of inversion sequences of length n avoiding the consecutive patterns 010, 021, and 120.

1, 1, 2, 5, 15, 53, 216, 994, 5076, 28403, 172538, 1129511, 7919314, 59150556, 468504022, 3919569708, 34518111783, 319030219223, 3086250047021, 31174921402976, 328110078110137, 3591110146030066, 40800503952916639, 480429785491094856, 5854374278697301978

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, and 120.

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 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, i > x)), 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, i > x]], {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, A328431, A328433, A328434, A328435, A328436, A328437, A328438, A328439, A328440, A328441, A328442.

Sequence in context: A328431 A120567 A263779 * A337850 A125280 A338728

Adjacent sequences: A328429 A328430 A328431 * A328433 A328434 A328435

Keyword

nonn

Author

Juan S. Auli, Oct 16 2019

Status

approved