A136776 Number of primitive multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.

1, 2, 6, 17, 48, 135, 379, 1063, 2980, 8352, 23405, 65584, 183769, 514919, 1442785, 4042614, 11327182, 31738101, 88928244, 249171491, 698163131, 1956209807, 5481178344, 15357920824, 43031938457, 120572813012, 337837515853, 946599685919, 2652313383105

Offset: 1

Author

Steve Butler, Jan 21 2008

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.
• Index entries for linear recurrences with constant coefficients, signature (4,-3,-1).

Crossrefs

Cf. A136775.

Programs

Mathematica

Rest[CoefficientList[Series[(x-2x^2+x^3)/(1-4x+3x^2+x^3),{x,0,40}],x]] (* or *) LinearRecurrence[{4,-3,-1},{1,2,6},40] (* Harvey P. Dale, Sep 17 2013 *)

PARI

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

Formula

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

a(1)=1, a(2)=2, a(3)=6, a(n) = 4*a(n-1)-3*a(n-2)-a(n-3). - Harvey P. Dale, Sep 17 2013