|
|
A136779
|
|
Number of multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2.
|
|
2
|
|
|
1, 3, 18, 105, 606, 3483, 19986, 114609, 657054, 3766515, 21590418, 123758649, 709393758, 4066287627, 23308182162, 133603718145, 765823377054, 4389738680547, 25162205542674, 144231041494281, 826739659899486, 4738913739770235, 27163694339468562
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1-5*x+7*x^2)/(1-8*x+13*x^2).
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|