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A136775 Number of multiplex juggling sequences of length n, base state <1,1> and hand capacity 2. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
LINKS
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
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
MATHEMATICA
CoefficientList[Series[(x^2-2x+1)/(5x^2-5x+1), {x, 0, 30}], x] (* Harvey P. Dale, Jun 22 2014 *)
PROG
(PARI) Vec((x-2*x^2+x^3)/(1-5*x+5*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016
(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
CROSSREFS
Cf. A136776.
Sequence in context: A149062 A066979 A333548 * A108153 A010911 A052941
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 21 2008
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)