

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
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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*x15)*x/(3*x1).  Alois P. Heinz, Oct 17 2017
From Colin Barker, Oct 18 2017: (Start)
a(n) = 292*3^(n4) for n>3.
a(n) = 3*a(n1) 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



