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A136776 Number of primitive multiplex juggling sequences of length n, base state <1,1> and hand capacity 2. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)