A136775 Number of multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
1, 3, 11, 40, 145, 525, 1900, 6875, 24875, 90000, 325625, 1178125, 4262500, 15421875, 55796875, 201875000, 730390625, 2642578125, 9560937500, 34591796875, 125154296875, 452812500000, 1638291015625, 5927392578125, 21445507812500, 77590576171875
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Carolina Benedetti, Christopher R. H. Hanusa, Pamela E. Harris, Alejandro H. Morales, Anthony Simpson, Kostant's partition function and magic multiplex juggling sequences, arXiv:2001.03219 [math.CO], 2020. See Table 1 p. 12.
- S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.
- P. E. Harris, E. Insko, L. K. Williams, The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula, arXiv preprint arXiv:1401.0055, 2014
- Index entries for linear recurrences with constant coefficients, signature (5,-5).
Crossrefs
Cf. A136776.
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 27); Coefficients(R!( (x-2*x^2+x^3)/(1-5*x+5*x^2))); // Marius A. Burtea, Jan 13 2020 -
Mathematica
CoefficientList[Series[(x^2-2x+1)/(5x^2-5x+1),{x,0,30}],x] (* Harvey P. Dale, Jun 22 2014 *) -
PARI
Vec((x-2*x^2+x^3)/(1-5*x+5*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016
Formula
G.f.: (x-2x^2+x^3)/(1-5x+5x^2).
a(n) = 5*a(n-1)-5*a(n-2) for n>3. - Colin Barker, Aug 31 2016
Comments