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A293156 Number of linear chord diagrams with n+2 chords such that every chord has length at least n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 03:48 EST 2021. Contains 349417 sequences. (Running on oeis4.)