A279570 Number of length n inversion sequences avoiding the patterns 110 and 120.

1, 1, 2, 6, 22, 92, 423, 2091, 10950, 60120, 343453, 2029809, 12354661, 77168197, 493189283, 3217459119, 21382723456, 144518555231, 991885282987, 6904454991721, 48691257834999, 347542736059492, 2508603139285095, 18297609829743478, 134772911886028731

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 110 and 120.

Links

Benjamin Testart, Table of n, a(n) for n = 0..350

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

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

Example

The length 4 inversion sequences avoiding (110,120) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 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, A279571, A279572, A279573.

Sequence in context: A342291 A001181 A130579 * A338748 A107945 A279571

Adjacent sequences: A279567 A279568 A279569 * A279571 A279572 A279573

Keyword

nonn

Author

Megan A. Martinez, Feb 21 2017

Extensions

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

Status

approved