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

1,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A136775.

Sequence in context: A292229 A090039 A299166 * A018915 A019487 A077936

Adjacent sequences: A136773 A136774 A136775 * A136777 A136778 A136779

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved