A279573 Number of length n inversion sequences avoiding the patterns 120 and 210.

1, 1, 2, 6, 23, 102, 499, 2625, 14601, 84847, 510614, 3161964, 20050770, 129718404, 853689031, 5701759424, 38574689104, 263936457042, 1824032887177, 12718193293888, 89386742081688, 632746535420834, 4508140253686638, 32308561883462867, 232790342330880572

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 and 210.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

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

Chunyan Yan, Zhicong Lin, Inversion sequences avoiding pairs of patterns, arXiv:1912.03674 [math.CO], 2019.

Formula

a(n) ~ c * 8^n / n^(3/2), where c = 0.0013548789253263217919... - Vaclav Kotesovec, Oct 07 2021

Example

The length 4 inversion sequences avoiding (120,210) 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

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572.

Sequence in context: A088929 A356111 A374550 * A174193 A238639 A226995

Adjacent sequences: A279570 A279571 A279572 * A279574 A279575 A279576

Keyword

nonn

Author

Megan A. Martinez, Feb 21 2017

Extensions

a(10)-a(24) from Alois P. Heinz, Feb 21 2017

Status

approved