A136784 Number of primitive multiplex juggling sequences of length n, base state <3> and hand capacity 3.

1, 3, 13, 67, 369, 2083, 11869, 67875, 388705, 2227267, 12764973, 73165315, 419377873, 2403873891, 13779078781, 78982269667, 452730133185, 2595071559811, 14875080747085, 85264715699139, 488741675881009, 2801492102959267, 16058295037221021, 92046962959297699

Offset

1,2

Links

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

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

Index entries for linear recurrences with constant coefficients, signature (9,-21,13).

Formula

G.f.: (x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3).

From Colin Barker, Aug 31 2016: (Start)

a(n) = (13+(4-sqrt(3))^n*(4+sqrt(3))-(-4+sqrt(3))*(4+sqrt(3))^n)/39.

a(n) = 9*a(n-1)-21*a(n-2)+13*a(n-3) for n>3.

(End)

Example

a(2)=3 since <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the three possibilities.

Prog

(PARI) Vec((x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016

Crossrefs

Cf. A136783.

Sequence in context: A343204 A333083 A298611 * A284717 A027277 A242798

Adjacent sequences: A136781 A136782 A136783 * A136785 A136786 A136787

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved