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

Author

Megan A. Martinez, Jan 17 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_k. This is the same as the set of length n inversion sequences avoiding 010 and 120.

Examples

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

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.

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.

Extensions

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