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A136777 Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 2. 3
1, 4, 22, 124, 706, 4036, 23110, 132412, 758866, 4349572, 24931318, 142906108, 819141730, 4695354436, 26913992998, 154272336316, 884296781554, 5068833880324, 29054812882390, 166543662614908, 954636733448194, 5472026253591748, 31365932493907462 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, 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.

Index entries for linear recurrences with constant coefficients, signature (8,-13).

FORMULA

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

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

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

MATHEMATICA

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 *)

PROG

(PARI) Vec((x-4*x^2+3*x^3)/(1-8*x+13*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016

(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

CROSSREFS

Cf. A136778.

Sequence in context: A185858 A180034 A260346 * A056625 A116428 A121187

Adjacent sequences:  A136774 A136775 A136776 * A136778 A136779 A136780

KEYWORD

nonn,easy

AUTHOR

Steve Butler, Jan 21 2008

STATUS

approved

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)