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

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

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5, -6)

Formula

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

Mathematica

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

Prog

(PARI) 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

Crossrefs

A diagonal of A293881.

Cf. A257113, A293156.

Sequence in context: A192254 A368502 A220155 * A051966 A221568 A092774

Adjacent sequences: A321308 A321309 A321310 * A321312 A321313 A321314

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 17 2018

Status

approved