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

Author

Steve Butler, Jan 21 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A136778.

Programs

Magma

R:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-4*x^2+3*x^3)/(1-8*x+13*x^2))); // Marius A. Burtea, Jan 13 2020

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 *)

PARI

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

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