A279558 Number of length n inversion sequences avoiding the patterns 010, 120, and 210.

1, 1, 2, 5, 15, 52, 200, 830, 3654, 16869, 80963, 401300, 2043610, 10649335, 56604706, 306101789, 1680515427

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 010, 120, and 210.

Links

Table of n, a(n) for n=0..16.

Megan A. Martinez, Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016-2018.

Example

The length 4 inversion sequences avoiding (010, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Crossrefs

Cf. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A370798 A007312 A007296 * A224071 A202062 A279559

Adjacent sequences: A279555 A279556 A279557 * A279559 A279560 A279561

Keyword

nonn,more

Author

Megan A. Martinez, Jan 17 2017

Extensions

a(10)-a(12) from Alois P. Heinz, Feb 24 2017

a(13)-a(16) from Bert Dobbelaere, Dec 30 2018

Status

approved