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

Author

Megan A. Martinez, Feb 21 2017

Keywords

• nonn

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 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.

Examples

			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.
		

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.

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.

Formula

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

Extensions

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