A279559 -id:A279559 - cp's OEIS frontend

A279558 Number of length n inversion sequences avoiding the patterns 010, 120, and 210.

1, 1, 2, 5, 15, 52, 200, 830, 3654, 16869, 80963, 401300, 2043610, 10649335, 56604706, 306101789, 1680515427

Offset: 0

Megan A. Martinez, Jan 17 2017

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, 120, and 210.

			The length 4 inversion sequences avoiding (010, 120, 210) 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. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

a(10)-a(12) from Alois P. Heinz, Feb 24 2017

a(13)-a(16) 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

A374548 Number of length n inversion sequences avoiding the patterns 011 and 120.

Original entry on oeis.org

1, 1, 2, 5, 14, 42, 132, 431, 1452, 5026, 17808, 64398, 237097, 886935, 3365348, 12933691, 50285912, 197586405, 783922944, 3138088910, 12666148475, 51517864816, 211047556685, 870385025022, 3612193740355, 15079839929453, 63305470339527, 267159465034792

Offset: 0

Benjamin Testart, Jul 13 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..430
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A000110, A263778, A279555, A279559, A279570.

A374553 Number of length n inversion sequences avoiding the patterns 010 and 102.

Original entry on oeis.org

1, 1, 2, 5, 15, 51, 186, 707, 2763, 11024, 44714, 183830, 764374, 3209031, 13584217, 57918257, 248502212, 1072159593, 4648747281, 20245772943, 88524364619, 388469248937, 1710304847176, 7552480937589, 33442335151831, 148456424569164, 660560252794208

Offset: 0

Benjamin Testart, Jul 17 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..700
Jay Pantone, The enumeration of inversion sequences avoiding the patterns 201 and 210, arXiv:2310.19632 [math.CO], 2023.
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.
Benjamin Testart, Generating trees growing on the left for pattern-avoiding inversion sequences, arXiv:2411.05726 [math.CO], 2024.

Cf. A200753, A263779, A279559, A279566, A374541, A374542.

G.f. F(x) is algebraic with minimal polynomial x * (x^2 - x + 1)*(x - 1)^2 * F(x)^3 + 2*x*(x - 1)*(2*x^2 - 2*x + 1)*F(x)^2 - (x^4 - 8*x^3 + 11*x^2 - 6*x + 1)*F(x) - (2*x - 1)*(x - 1)^2.

A374549 Number of length n inversion sequences avoiding the patterns 100 and 120.

Original entry on oeis.org

1, 1, 2, 6, 22, 92, 421, 2062, 10646, 57324, 319436, 1831585, 10758458, 64513454, 393846399, 2442328993, 15356020884, 97741913382, 628994116349, 4087863691061, 26805206933158, 177198351316543, 1180073345351131, 7912190584017869, 53380776660751987

Offset: 0

Benjamin Testart, Jul 17 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..350
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A263778, A263780, A279559, A279564, A279570, A374544.

A374550 Number of length n inversion sequences avoiding the patterns 120 and 201.

Original entry on oeis.org

1, 1, 2, 6, 23, 102, 498, 2607, 14386, 82663, 490228, 2981407, 18507513, 116855873, 748427848, 4851982365, 31784721142, 210111119681, 1399977460914, 9393523464391, 63420812374620, 430570197000992, 2937789342516835, 20135022976572246, 138566149670814993

Offset: 0

Benjamin Testart, Jul 17 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..350
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A263777, A263778, A279559, A279566, A279570, A360052, A374546, A374548.

A374552 Number of length n inversion sequences avoiding the patterns 000 and 120.

Original entry on oeis.org

1, 1, 2, 5, 15, 50, 185, 737, 3126, 13976, 65426, 318699, 1607800, 8368088, 44791046, 245903077, 1381505822, 7926881015, 46373681595, 276193339071, 1672469062126, 10284954435831, 64164864206704, 405733694376937, 2598199309906531, 16837017409254863

Offset: 0

Benjamin Testart, Jul 17 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..360
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A000111, A263778, A279552, A279559, A279564, A279570, A374541, A374543.

cp's OEIS Frontend

A279558 Number of length n inversion sequences avoiding the patterns 010, 120, and 210.

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

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A374548 Number of length n inversion sequences avoiding the patterns 011 and 120.

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A374553 Number of length n inversion sequences avoiding the patterns 010 and 102.

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A374549 Number of length n inversion sequences avoiding the patterns 100 and 120.

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A374550 Number of length n inversion sequences avoiding the patterns 120 and 201.

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A374552 Number of length n inversion sequences avoiding the patterns 000 and 120.

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