A279564 -id:A279564 - 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

A374545 Number of length n inversion sequences avoiding the patterns 100 and 101.

Original entry on oeis.org

1, 1, 2, 6, 22, 93, 439, 2267, 12628, 75119, 473610, 3146376, 21923158, 159610880, 1210421617, 9536525715, 77885388296, 658112437816, 5743744103287, 51701114086088, 479340725109862, 4572111104329002, 44818226981293308, 451062570619242508, 4656687307250419533

Offset: 0

Benjamin Testart, Jul 12 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..580
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A113227, A263780, A279564, A279570, A374544.

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.

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.

A374554 Number of length n inversion sequences avoiding the patterns 100 and 102.

Original entry on oeis.org

1, 1, 2, 6, 21, 80, 318, 1305, 5487, 23535, 102603, 453400, 2026408, 9144361, 41607161, 190675552, 879318056, 4077566276, 19001732690, 88940105945, 417948841012, 1971086634986, 9326180071850, 44258248464408, 210605264950063, 1004694354945863, 4804017049287049

Offset: 0

Benjamin Testart, Jul 17 2024

nonn

Benjamin Testart, Table of n, a(n) for n = 0..400
Benjamin Testart, Completing the enumeration of inversion sequences avoiding one or two patterns of length 3, arXiv:2407.07701 [math.CO], 2024.

Cf. A200753, A263780, A279564, A279566, A374541, A374542, A374544, A374545, A374553.

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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A374545 Number of length n inversion sequences avoiding the patterns 100 and 101.

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

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

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A374554 Number of length n inversion sequences avoiding the patterns 100 and 102.

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