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Number of primitive multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
3

%I #12 Aug 31 2016 09:06:59

%S 1,2,6,17,48,135,379,1063,2980,8352,23405,65584,183769,514919,1442785,

%T 4042614,11327182,31738101,88928244,249171491,698163131,1956209807,

%U 5481178344,15357920824,43031938457,120572813012,337837515853,946599685919,2652313383105

%N Number of primitive multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.

%H Colin Barker, <a href="/A136776/b136776.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 (4,-3,-1).

%F G.f.: (x-2*x^2+x^3)/(1-4*x+3*x^2+x^3).

%F a(1)=1, a(2)=2, a(3)=6, a(n) = 4*a(n-1)-3*a(n-2)-a(n-3). - _Harvey P. Dale_, Sep 17 2013

%t Rest[CoefficientList[Series[(x-2x^2+x^3)/(1-4x+3x^2+x^3),{x,0,40}],x]] (* or *) LinearRecurrence[{4,-3,-1},{1,2,6},40] (* _Harvey P. Dale_, Sep 17 2013 *)

%o (PARI) Vec((x-2*x^2+x^3)/(1-4*x+3*x^2+x^3) + O(x^30)) \\ _Colin Barker_, Aug 31 2016

%Y Cf. A136775.

%K nonn,easy

%O 1,2

%A _Steve Butler_, Jan 21 2008