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 and 010.
LINKS
Benjamin Testart, Table of n, a(n) for n = 0..200
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Benjamin Testart, Inversion sequences avoiding the pattern 010, arXiv:2212.07222 [math.CO], 2022.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
EXAMPLE
For n=3, the inversion sequences are 001, 002, 011, 012.
For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.
CROSSREFS
KEYWORD
nonn
AUTHOR
Megan A. Martinez, Dec 15 2016
EXTENSIONS
a(10)-a(20) from Alois P. Heinz, Feb 23 2017
a(21) onwards from Benjamin Testart, Feb 01 2023
STATUS
approved