A136783 Number of multiplex juggling sequences of length n, base state <3> and hand capacity 3.

1, 4, 20, 112, 660, 3976, 24180, 147648, 903140, 5528504, 33853220, 207325392, 1269787060, 7777149416, 47633751380, 291750220768, 1786933908740, 10944758154264, 67035370422020, 410583912229872, 2514779283989460, 15402734618128456, 94339983758166580

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 (10,-27,20).

Formula

G.f.: (x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3).

a(n) = 10*a(n-1)-27*a(n-2)+20*a(n-3) for n>3. - Colin Barker, Aug 31 2016

Example

a(2)=4 since <3> -> <3> -> <3>; <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the four possibilities.

Mathematica

LinearRecurrence[{10, -27, 20}, {1, 4, 20}, 30] (* Harvey P. Dale, Sep 17 2020 *)

Prog

(PARI) Vec((x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3))); // Marius A. Burtea, Jan 13 2020

Crossrefs

Cf. A136784.

Sequence in context: A153299 A239643 A081335 * A227726 A080609 A003645

Adjacent sequences: A136780 A136781 A136782 * A136784 A136785 A136786

Keyword

nonn,easy

Author

Steve Butler, Jan 21 2008

Status

approved