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A279571

Number of length n inversion sequences avoiding the patterns 100, 101, and 201.

1, 1, 2, 6, 22, 92, 424, 2106, 11102, 61436, 353980, 2110366, 12955020, 81569168, 525106698, 3447244188, 23028080268, 156246994264, 1075127143948, 7492458675666, 52820934349420, 376331681648402, 2707312468516446, 19650530699752470, 143807774782994412, 1060472244838174574, 7875713244761349666, 58876660310205135380, 442862775457168812898, 3350397169412102710198

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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_i > e_j <= e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 100, 101, and 201.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..32

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

EXAMPLE

The length 4 inversion sequences avoiding (100,101,201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0102, 0103, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123.

MAPLE

b:= proc(n, i, s, m) option remember;

`if`(n=0, 1, add(b(n-1, i+1, s minus {$j..m-

`if`(j=m, 1, 0)} union {i+1}, max(m, j)), j=s))

end:

a:= n-> b(n, 1, {1}, 0):

seq(a(n), n=0..15); # Alois P. Heinz, Feb 22 2017

MATHEMATICA

b[n_, i_, s_, m_] := b[n, i, s, m] = If[n == 0, 1, Sum[b[n-1, i+1, s ~Complement~ Range[j, m - If[j == m, 1, 0]] ~Union~ {i+1}, Max[m, j]], {j, s}]];

a[n_] := b[n, 1, {1}, 0];

Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Oct 27 2017, after Alois P. Heinz *)

CROSSREFS