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A279544 Number of length n inversion sequences avoiding the patterns 000, 010, 110, 120, and 210. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

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-Fran├žois Alcover, Nov 10 2017, after Alois P. Heinz *)

CROSSREFS

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

Sequence in context: A210043 A049130 A101488 * A245898 A230662 A206464

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

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)