A279559 Number of length n inversion sequences avoiding the patterns 010 and 120.

1, 1, 2, 5, 15, 52, 201, 845, 3801, 18089, 90316, 470010, 2536077, 14127741, 80966690, 475979359, 2863157581, 17585971037, 110095460224, 701418693025, 4541497543092, 29847982448766, 198913925919741, 1342890255133042, 9176456969273844, 63422002415068463

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 and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010 and 120.

Links

Benjamin Testart, Table of n, a(n) for n = 0..400

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, Inversion sequences avoiding the pattern 010, arXiv:2212.07222 [math.CO], 2022.

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

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

Example

The length 4 inversion sequences avoiding (010, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Crossrefs

Cf. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A279558 A224071 A202062 * A359191 A056272 A140980

Adjacent sequences: A279556 A279557 A279558 * A279560 A279561 A279562

Keyword

nonn

Author

Megan A. Martinez, Jan 17 2017

Extensions

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

Status

approved