A279558 -id:A279558 - cp's OEIS frontend

A279554 Number of length n inversion sequences avoiding the patterns 010, 101, 120, 201, and 210.

1, 1, 2, 5, 15, 51, 188, 733, 2979, 12495, 53708, 235396, 1048168, 4728757, 21569339, 99309057, 460932778, 2154402107

Offset: 0

Megan A. Martinez, Dec 15 2016

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_j <> e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 101, 120, 201, and 210.

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

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

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

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

a(12)-a(17) from Bert Dobbelaere, Dec 30 2018

A279572 Number of length n inversion sequences avoiding the patterns 120, 201, and 210.

Original entry on oeis.org

1, 1, 2, 6, 23, 101, 484, 2468, 13166, 72630, 411076, 2374188, 13938018, 82932254, 499031324, 3031610924, 18568429963, 114541486785, 710973143614, 4437415155234, 27831038618735, 175318861863701, 1108762012137252, 7037137177329268, 44808588430903068

Offset: 0

Megan A. Martinez, Feb 21 2017

nonn

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_j <> e_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 120, 201, and 210.

			The length 4 inversion sequences avoiding (120, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0110, 0111, 0112, 0113, 0121, 0122, 0123.

Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 4.3 at page 16.
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.

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, A279570, A279571, A279573.

a(12)-a(15) from Bert Dobbelaere, Dec 30 2018

a(16)-a(24) from Toufik Mansour et al. added by Stefano Spezia, Jan 20 2024

cp's OEIS Frontend

A279554 Number of length n inversion sequences avoiding the patterns 010, 101, 120, 201, and 210.

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