A279554 Number of length n inversion sequences avoiding the patterns 010, 101, 120, 201, and 210.

1, 1, 2, 5, 15, 51, 188, 733, 2979, 12495, 53708, 235396, 1048168, 4728757, 21569339, 99309057, 460932778, 2154402107

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, 101, 120, 201, and 210.

Links

Table of n, a(n) for n=0..17.

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 3 inversion sequences are 000, 001, 002, 011, 012.
The length 4 inversion sequences are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A366096 A007317 A181768 * A279555 A153197 A299968

Adjacent sequences: A279551 A279552 A279553 * A279555 A279556 A279557

Keyword

nonn,more

Author

Megan A. Martinez, Dec 15 2016

Extensions

a(10)-a(11) from Alois P. Heinz, Feb 24 2017

a(12)-a(17) from Bert Dobbelaere, Dec 30 2018

Status

approved