A293156 Number of linear chord diagrams with n+2 chords such that every chord has length at least n.

15, 36, 99, 292, 876, 2628, 7884, 23652, 70956, 212868, 638604, 1915812, 5747436, 17242308, 51726924, 155180772, 465542316, 1396626948, 4189880844, 12569642532, 37708927596, 113126782788, 339380348364, 1018141045092, 3054423135276, 9163269405828, 27489808217484

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Everett Sullivan, Linear chord diagrams with long chords, arXiv preprint arXiv:1611.02771 [math.CO], 2016.

Index entries for linear recurrences with constant coefficients, signature (3).

Formula

G.f.: (5*x^3+9*x^2+9*x-15)*x/(3*x-1). - Alois P. Heinz, Oct 17 2017

From Colin Barker, Oct 18 2017: (Start)

a(n) = 292*3^(n-4) for n>3.

a(n) = 3*a(n-1) for n>4.

(End)

Mathematica

Join[{15, 36, 99}, NestList[3#&, 292, 30]] (* Harvey P. Dale, Sep 25 2018 *)

Prog

(PARI) Vec(x*(15 - 9*x - 9*x^2 - 5*x^3) / (1 - 3*x) + O(x^30)) \\ Colin Barker, Oct 18 2017

Crossrefs

A diagonal of A293157.

Sequence in context: A166146 A229235 A346881 * A329909 A118867 A260796

Adjacent sequences: A293153 A293154 A293155 * A293157 A293158 A293159

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 10 2017

Extensions

More terms from Alois P. Heinz, Oct 17 2017

Status

approved