A136779 Number of multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2.

1, 3, 18, 105, 606, 3483, 19986, 114609, 657054, 3766515, 21590418, 123758649, 709393758, 4066287627, 23308182162, 133603718145, 765823377054, 4389738680547, 25162205542674, 144231041494281, 826739659899486, 4738913739770235, 27163694339468562

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Carolina Benedetti, Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, and Anthony Simpson, Kostant's partition function and magic multiplex juggling sequences, arXiv:2001.03219 [math.CO], 2020. See Table 1 p. 12.

S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.

Index entries for linear recurrences with constant coefficients, signature (8,-13).

Formula

G.f.: x*(1-5*x+7*x^2)/(1-8*x+13*x^2).

From Colin Barker, Aug 31 2016: (Start)

a(n) = 8*a(n-1)-13*a(n-2) for n>3.

a(n) = ((9-14*sqrt(3))*(4-sqrt(3))^n+(4+sqrt(3))^n*(9+14*sqrt(3)))/338 for n>1. (End)

E.g.f.: (91*x - 9 + exp(4*x)*(9*cosh(sqrt(3)*x) + 14*sqrt(3)*sinh(sqrt(3)*x)))/169. - Stefano Spezia, Oct 15 2023

Mathematica

LinearRecurrence[{8, -13}, {1, 3, 18}, 25] (* Paolo Xausa, Oct 24 2023 *)

Prog

(PARI) Vec((x-5*x^2+7*x^3)/(1-8*x+13*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-5*x^2+7*x^3)/(1-8*x+13*x^2))); // Marius A. Burtea, Jan 13 2020

Crossrefs

Cf. A136780.

Sequence in context: A009021 A303519 A124408 * A106328 A007277 A025595

Adjacent sequences: A136776 A136777 A136778 * A136780 A136781 A136782

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved