A279544 Number of length n inversion sequences avoiding the patterns 000, 010, 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

0,3

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<j<k) such that e_j >= e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 000, 010, 110, 120, and 210.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..600

Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A210043 A049130 A101488 * A245898 A230662 A351642

Adjacent sequences: A279541 A279542 A279543 * A279545 A279546 A279547

Keyword

nonn

Author

Megan A. Martinez, Dec 14 2016

Extensions

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

Status

approved