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A136784
Number of primitive multiplex juggling sequences of length n, base state <3> and hand capacity 3.
2
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
S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.
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
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 21 2008
STATUS
approved