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 120, 201, and 210.
LINKS
Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 4.3 at page 16.
Megan A. Martinez and 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 (120, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0110, 0111, 0112, 0113, 0121, 0122, 0123.
CROSSREFS
KEYWORD
nonn
AUTHOR
Megan A. Martinez, Feb 21 2017
EXTENSIONS
a(12)-a(15) from Bert Dobbelaere, Dec 30 2018
a(16)-a(24) from Toufik Mansour et al. added by Stefano Spezia, Jan 20 2024
STATUS
approved