A136775 - OEIS

%I #30 Sep 08 2022 08:45:32

%S 1,3,11,40,145,525,1900,6875,24875,90000,325625,1178125,4262500,

%T 15421875,55796875,201875000,730390625,2642578125,9560937500,

%U 34591796875,125154296875,452812500000,1638291015625,5927392578125,21445507812500,77590576171875

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

%C Except for the initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = 1 - 3 S + S^2; see A291000.  - _Clark Kimberling_, Aug 24 2017

%H Vincenzo Librandi, <a href="/A136775/b136775.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 P. E. Harris, E. Insko, L. K. Williams, <a href="http://arxiv.org/abs/1401.0055">The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula</a>, arXiv preprint arXiv:1401.0055, 2014

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5).

%F G.f.: (x-2x^2+x^3)/(1-5x+5x^2).

%F a(n) = 5*a(n-1)-5*a(n-2) for n>3. - _Colin Barker_, Aug 31 2016

%t CoefficientList[Series[(x^2-2x+1)/(5x^2-5x+1),{x,0,30}],x] (* _Harvey P. Dale_, Jun 22 2014 *)

%o (PARI) Vec((x-2*x^2+x^3)/(1-5*x+5*x^2) + O(x^30)) \\ _Colin Barker_, Aug 31 2016

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 27); Coefficients(R!( (x-2*x^2+x^3)/(1-5*x+5*x^2))); // _Marius A. Burtea_, Jan 13 2020

%Y Cf. A136776.

%K nonn,easy

%O 1,2

%A _Steve Butler_, Jan 21 2008