cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

1, 1, 2, 5, 15, 52, 200, 830, 3654, 16869, 80963, 401300, 2043610, 10649335, 56604706, 306101789, 1680515427
Offset: 0

Views

Author

Megan A. Martinez, Jan 17 2017

Keywords

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 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.

Examples

			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.

Links

Crossrefs

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.

Extensions

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

Views

Author

Megan A. Martinez, Feb 21 2017

Keywords

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 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.

Examples

			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.

Links

Crossrefs

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.

Extensions

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

A374542 Number of length n inversion sequences avoiding the patterns 102 and 210.

Original entry on oeis.org

1, 1, 2, 6, 22, 87, 351, 1416, 5681, 22660, 89961, 355924, 1404839, 5536143, 21794634, 85749490, 337271186, 1326421512, 5216761708, 20520185594, 80733298320, 317713643536, 1250674963766, 4924782835110, 19398524629494, 76434881013402, 301270165265954
Offset: 0

Views

Author

Benjamin Testart, Jul 12 2024

Keywords

Links

Crossrefs

Cf. A279555.

Formula

G.f: ((4*x - 1) * (4*x^4 - 22*x^3 + 25*x^2 - 9*x + 1) - (2*x - 1) * (x^2 - 5*x + 1) * (2*x^2 - 4*x + 1) * (1-4*x)^(1/2)) / (2*x^3 * (4*x - 1) * (x - 1)^2).
D-finite with recurrence -(n+3)*(1514*n-13441)*a(n) +(16281*n^2-104929*n-159699)*a(n-1) +(-54702*n^2+377288*n-136533)*a(n-2) +(60299*n^2-430394*n+520290)*a(n-3) -6*(2*n-7)*(1697*n-7015)*a(n-4) +30*(-702*n+3361)=0. - R. J. Mathar, Jul 12 2024
a(n) ~ 2^(2*n+1)/(3*sqrt(Pi*n)). - Vaclav Kotesovec, Nov 21 2024

A374543 Number of length n inversion sequences avoiding the patterns 000 and 201 (or 000 and 210).

Original entry on oeis.org

1, 1, 2, 5, 16, 60, 257, 1218, 6270, 34530, 201223, 1230168, 7836622, 51738649, 352457285, 2468427794, 17718840472, 130027678901, 973357030743, 7418717413322, 57477823445999, 452035218046890, 3604179615488962, 29102380883498470, 237748924887335003
Offset: 0

Views

Author

Benjamin Testart, Jul 12 2024

Keywords

Links

Crossrefs

Cf. A279555.

A374544 Number of length n inversion sequences avoiding the patterns 100 and 110.

Original entry on oeis.org

1, 1, 2, 6, 22, 93, 437, 2233, 12227, 71011, 434151, 2778424, 18530560, 128351696, 920714033, 6824472471, 52169690544, 410668022430, 3324392442855, 27643496374175, 235891305666644, 2063970414061799, 18503192136038026, 169846619393391680, 1595434723902554826
Offset: 0

Views

Author

Benjamin Testart, Jul 12 2024

Keywords

Links

Crossrefs

Cf. A279555.

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

Views

Author

Benjamin Testart, Jul 13 2024

Keywords

Links

Crossrefs

Cf. A000110, A263778, A279555, A279559, A279570.
Previous Showing 21-26 of 26 results.

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