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%I #16 Sep 08 2022 08:45:32
%S 1,4,20,112,660,3976,24180,147648,903140,5528504,33853220,207325392,
%T 1269787060,7777149416,47633751380,291750220768,1786933908740,
%U 10944758154264,67035370422020,410583912229872,2514779283989460,15402734618128456,94339983758166580
%N Number of multiplex juggling sequences of length n, base state <3> and hand capacity 3.
%H Colin Barker, <a href="/A136783/b136783.txt">Table of n, a(n) for n = 1..1000</a>
%H Carolina Benedetti, Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, Anthony Simpson, <a href="https://arxiv.org/abs/2001.03219">Kostant's partition function and magic multiplex juggling sequences</a>, arXiv:2001.03219 [math.CO], 2020. See Table 1 p. 12.
%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 (10,-27,20).
%F G.f.: (x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3).
%F a(n) = 10*a(n-1)-27*a(n-2)+20*a(n-3) for n>3. - _Colin Barker_, Aug 31 2016
%e a(2)=4 since <3> -> <3> -> <3>; <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the four possibilities.
%t LinearRecurrence[{10,-27,20},{1,4,20},30] (* _Harvey P. Dale_, Sep 17 2020 *)
%o (PARI) Vec((x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3) + O(x^30)) \\ _Colin Barker_, Aug 31 2016
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3))); // _Marius A. Burtea_, Jan 13 2020
%Y Cf. A136784.
%K nonn,easy
%O 1,2
%A _Steve Butler_, Jan 21 2008
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