A279556 Number of length n inversion sequences avoiding the patterns 010, 110, and 120.

1, 1, 2, 5, 15, 51, 190, 759, 3206, 14180, 65203, 309998, 1517330, 7619541, 39145113, 205261890, 1096393056, 5955598301, 32852080738, 183797522935, 1041802426740, 5977047039743, 34679912608313, 203345277644481, 1204104271508239, 7196256426157901

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 010, 110, and 120.

Links

Nicholas R. Beaton, Table of n, a(n) for n = 0..1000

Nathan Britt and Nicholas Beaton, Completing the enumeration of inversion sequences avoiding triples of relations, arXiv:2512.21943 [math.CO], 2025. See p. 3.

Megan A. Martinez and Carla D. Savage, Patterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations, arXiv:1609.08106 [math.CO], 2016-2018.

Example

The length 3 inversion sequences avoiding (010, 110, 120) are 000, 001, 002, 011, 012
The length 4 inversion sequences avoiding (010, 110, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Sequence in context: A279555 A153197 A299968 * A108307 A275605 A193296

Adjacent sequences: A279553 A279554 A279555 * A279557 A279558 A279559

Keyword

nonn

Author

Megan A. Martinez, Dec 16 2016

Extensions

a(10)-a(11) from Alois P. Heinz, Feb 24 2017

a(12)-a(16) from Bert Dobbelaere, Dec 30 2018

a(17)-a(25) from Nicholas R. Beaton, Aug 29 2025

Status

approved