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 010, 110, 120, and 210.
It can be shown that this sequence also counts the 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, 100, 120, and 210.
LINKS
Jay Pantone, Table of n, a(n) for n = 0..500
Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016.
Chunyan Yan and Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.
EXAMPLE
The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012.
The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.
CROSSREFS
KEYWORD
nonn
AUTHOR
Megan A. Martinez, Dec 16 2016
EXTENSIONS
a(10)-a(26) from Alois P. Heinz, Jan 05 2017
STATUS
approved