A293881 -id:A293881 - cp's OEIS frontend

A293920 Number of linear chord diagrams having n chords and minimal chord length seven.

1, 159, 7564, 245964, 6996588, 193799140, 5489211751, 162272284974, 5047554996855, 165595774518042, 5728636935767404, 208700950019470460, 7993330299623656154, 321268248361695869991, 13525506763517368392668, 595415097485805608016210, 27361311228606445955339071

Offset: 7

Alois P. Heinz, Oct 19 2017

nonn

Alois P. Heinz, Table of n, a(n) for n = 7..405

Column k=7 of A293881.

a(n) ~ (exp(-6) - exp(-7)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017

A293921 Number of linear chord diagrams having n chords and minimal chord length eight.

Original entry on oeis.org

1, 319, 23012, 1007508, 35994000, 1189202172, 38767936708, 1287523504769, 44237669097482, 1583944615087121, 59277212496035478, 2320361242104891484, 94969568142679887216, 4060520653281063962444, 181153019365969689229302, 8422282201884215125698329

Offset: 8

Alois P. Heinz, Oct 19 2017

nonn

Alois P. Heinz, Table of n, a(n) for n = 8..300

Column k=8 of A293881.

a(n) ~ (exp(-7) - exp(-8)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017

A293922 Number of linear chord diagrams having n chords and minimal chord length nine.

Original entry on oeis.org

1, 639, 69676, 4100988, 184283856, 7306919616, 275875184700, 10345618038532, 394140369614751, 15439822086531614, 625906719760828175, 26339564820084748490, 1152078058596976970932, 52386933718575091061064, 2475581777015155231108104, 121493777824620584462513636

Offset: 9

Alois P. Heinz, Oct 19 2017

nonn

Alois P. Heinz, Table of n, a(n) for n = 9..200

Column k=9 of A293881.

a(n) ~ (exp(-8) - exp(-9)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017

A293923 Number of linear chord diagrams having n chords and minimal chord length ten.

Original entry on oeis.org

1, 1279, 210308, 16616820, 938674704, 44808906240, 1968764070096, 83741573885052, 3550701549583204, 152621531791333545, 6715538352190953498, 304192204692846166233, 14228203377114098086822, 688242816096454213285132, 34448710283688839203990152

Offset: 10

Alois P. Heinz, Oct 19 2017

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..200

Column k=10 of A293881.

a(n) ~ (exp(-9) - exp(-10)) * 2^(n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Oct 25 2017

A290688 Number of linear chord diagrams having 2n chords and minimal chord length n.

Original entry on oeis.org

1, 2, 26, 854, 52938, 5317342, 788783482, 162272284974, 44237669097482, 15439822086531614, 6715538352190953498, 3561963935537880874894, 2263250481436117389497386, 1697243825672918269588268286, 1483337827671250048404238399034, 1494549066141865576239455292770414

Offset: 0

Alois P. Heinz, Oct 18 2017

nonn

Cf. A293881.

a(n) = A293881(2n,n).

A321311 Number of linear chord diagrams having n+2 chords and minimal chord length n.

Original entry on oeis.org

10, 26, 79, 252, 796, 2468, 7564, 23012, 69676, 210308, 633484, 1905572, 5726956, 17201348, 51645004, 155016932, 465214636, 1395971588, 4188570124, 12567021092, 37703684716, 113116297028, 339359376844, 1018099102052, 3054339249196, 9163101633668, 27489472673164

Offset: 1

Seiichi Manyama, Nov 17 2018

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5, -6)

A diagonal of A293881.

Cf. A257113, A293156.

Join[{10, 26, 79}, LinearRecurrence[{5, -6}, {252, 796}, 24]] (* Jean-François Alcover, Nov 24 2018 *)

Vec((10 - 24*x + 9*x^2 + 13*x^3 + 10*x^4)/((1 - 2*x)*(1 - 3*x)) + O(x^40)) \\ Andrew Howroyd, Nov 17 2018

a(n) = A293881(n+2,n).
a(n) = 5*a(n-1) - 6*a(n-2) for n > 5.
a(n) = A293156(n) - 5*2^(n-1).
G.f.: x*(10 - 24*x + 9*x^2 + 13*x^3 + 10*x^4)/((1 - 2*x)*(1 - 3*x)). - Andrew Howroyd, Nov 17 2018
2*3^4*a(n) = 2^3*73*3^n-5*3^4*2^n for n>3. - R. J. Mathar, Jan 25 2023

cp's OEIS Frontend

A293920 Number of linear chord diagrams having n chords and minimal chord length seven.

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A293921 Number of linear chord diagrams having n chords and minimal chord length eight.

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A293922 Number of linear chord diagrams having n chords and minimal chord length nine.

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A293923 Number of linear chord diagrams having n chords and minimal chord length ten.

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A290688 Number of linear chord diagrams having 2n chords and minimal chord length n.

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A321311 Number of linear chord diagrams having n+2 chords and minimal chord length n.

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