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%I #7 Aug 31 2016 07:55:17
%S 1,3,13,67,369,2083,11869,67875,388705,2227267,12764973,73165315,
%T 419377873,2403873891,13779078781,78982269667,452730133185,
%U 2595071559811,14875080747085,85264715699139,488741675881009,2801492102959267,16058295037221021,92046962959297699
%N Number of primitive multiplex juggling sequences of length n, base state <3> and hand capacity 3.
%H Colin Barker, <a href="/A136784/b136784.txt">Table of n, a(n) for n = 1..1000</a>
%H S. Butler and R. Graham, <a href="http://arXiv.org/abs/0801.2597">Enumerating (multiplex) juggling sequences</a>, arXiv:0801.2597 [math.CO], 2008.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-21,13).
%F G.f.: (x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3).
%F From _Colin Barker_, Aug 31 2016: (Start)
%F a(n) = (13+(4-sqrt(3))^n*(4+sqrt(3))-(-4+sqrt(3))*(4+sqrt(3))^n)/39.
%F a(n) = 9*a(n-1)-21*a(n-2)+13*a(n-3) for n>3.
%F (End)
%e a(2)=3 since <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the three possibilities.
%o (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
%Y Cf. A136783.
%K nonn,easy
%O 1,2
%A _Steve Butler_, Jan 21 2008
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