A136777 Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 2.

1, 4, 22, 124, 706, 4036, 23110, 132412, 758866, 4349572, 24931318, 142906108, 819141730, 4695354436, 26913992998, 154272336316, 884296781554, 5068833880324, 29054812882390, 166543662614908, 954636733448194, 5472026253591748, 31365932493907462

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