A279552 Number of length n inversion sequences avoiding the patterns 000 and 010.

1, 1, 2, 4, 10, 29, 95, 345, 1376, 5966, 27886, 139608, 744552, 4210191, 25140790, 157981820, 1041480482, 7183374125, 51711299169, 387683162541, 3020997261596, 24424884853963, 204559337781097, 1772011400733378, 15855597322378302, 146360032952969570

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_j >= e_k and e_i = e_k. This is the same as the set of length n inversion sequences avoiding 000 and 010.

Links

Benjamin Testart, Table of n, a(n) for n = 0..200

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.

Example

For n=3, the inversion sequences are 001, 002, 011, 012.
For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A086631 A320903 A230957 * A261041 A047051 A271077

Adjacent sequences: A279549 A279550 A279551 * A279553 A279554 A279555

Keyword

nonn

Author

Megan A. Martinez, Dec 15 2016

Extensions

a(10)-a(20) from Alois P. Heinz, Feb 23 2017

a(21) onwards from Benjamin Testart, Feb 01 2023

Status

approved