A136777 - OEIS

%I #19 Sep 08 2022 08:45:32

%S 1,4,22,124,706,4036,23110,132412,758866,4349572,24931318,142906108,

%T 819141730,4695354436,26913992998,154272336316,884296781554,

%U 5068833880324,29054812882390,166543662614908,954636733448194,5472026253591748,31365932493907462

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

%H Colin Barker, <a href="/A136777/b136777.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13).

%F G.f.: (x-4*x^2+3*x^3)/(1-8*x+13*x^2).

%F a(1)=1, a(2)=4, a(3)=22, a(n) = 8*a(n-1)-13*a(n-2). - _Harvey P. Dale_, Aug 26 2012

%F a(n) = ((4-sqrt(3))^n*(-9+14*sqrt(3))+(4+sqrt(3))^n*(9+14*sqrt(3)))/(169*sqrt(3)) for n>1. - _Colin Barker_, Aug 31 2016

%t Rest[CoefficientList[Series[(x-4x^2+3x^3)/(1-8x+13x^2),{x,0,30}],x]] (* or *) Join[{1},LinearRecurrence[{8,-13},{4,22},30]] (* _Harvey P. Dale_, Aug 26 2012 *)

%o (PARI) Vec((x-4*x^2+3*x^3)/(1-8*x+13*x^2) + O(x^30)) \\ _Colin Barker_, Aug 31 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-4*x^2+3*x^3)/(1-8*x+13*x^2))); // _Marius A. Burtea_, Jan 13 2020

%Y Cf. A136778.

%K nonn,easy

%O 1,2

%A _Steve Butler_, Jan 21 2008