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

1,2

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

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).

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

Adjacent sequences: A136772 A136773 A136774 * A136776 A136777 A136778

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved