A263780 Number of inversion sequences avoiding pattern 100.

1, 1, 2, 6, 23, 106, 565, 3399, 22678, 165646, 1311334, 11161529, 101478038, 980157177, 10011461983, 107712637346, 1216525155129, 14380174353934, 177440071258827, 2280166654498540, 30450785320307436, 421820687108853017, 6050801956624661417, 89738550379292147192

Offset

0,3

Comments

Number of length n inversion sequences avoiding e_i > e_j = e_k for i<j<k. A length n inversion sequence e_1,e_2,...,e_n consists of nonnegative integers e_t <= t-1. - Alois P. Heinz, Dec 19 2016

Links

Jay Pantone, Table of n, a(n) for n = 0..200

Sylvie Corteel, Megan A. Martinez, Carla D. Savage, and Michael Weselcouch, Patterns in Inversion Sequences I, arXiv:1510.05434 [math.CO], 2015.

Ilias Kotsireas, Toufik Mansour, and Gökhan Yıldırım, An Algorithmic Approach Based on Generating Trees for Enumerating Pattern-Avoiding Inversion Sequences, J. Symbolic Comput. 120 (2024), Paper No. 102231, 18 pp.

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

Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023.

Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024. See p. 2.

Crossrefs

Cf. A263777, A263778, A263779, A279544.

Sequence in context: A325297 A288912 A193321 * A363417 A125273 A336070

Adjacent sequences: A263777 A263778 A263779 * A263781 A263782 A263783

Keyword

nonn

Author

Michel Marcus, Oct 26 2015

Extensions

a(0)=1 prepended by Alois P. Heinz, Dec 15 2016

a(10)-a(23) from Alois P. Heinz, Dec 19 2016

Status

approved