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
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).
Crossrefs
A diagonal of A293157.
Programs
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Mathematica
Join[{15,36,99},NestList[3#&,292,30]] (* Harvey P. Dale, Sep 25 2018 *) -
PARI
Vec(x*(15 - 9*x - 9*x^2 - 5*x^3) / (1 - 3*x) + O(x^30)) \\ Colin Barker, Oct 18 2017
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)
Extensions
More terms from Alois P. Heinz, Oct 17 2017