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A136783
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Number of multiplex juggling sequences of length n, base state <3> and hand capacity 3.
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2
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1, 4, 20, 112, 660, 3976, 24180, 147648, 903140, 5528504, 33853220, 207325392, 1269787060, 7777149416, 47633751380, 291750220768, 1786933908740, 10944758154264, 67035370422020, 410583912229872, 2514779283989460, 15402734618128456, 94339983758166580
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OFFSET
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1,2
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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a(2)=4 since <3> -> <3> -> <3>; <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the four possibilities.
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MATHEMATICA
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LinearRecurrence[{10, -27, 20}, {1, 4, 20}, 30] (* Harvey P. Dale, Sep 17 2020 *)
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PROG
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(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
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CROSSREFS
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Cf. A136784.
Sequence in context: A153299 A239643 A081335 * A227726 A080609 A003645
Adjacent sequences: A136780 A136781 A136782 * A136784 A136785 A136786
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KEYWORD
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nonn,easy
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AUTHOR
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Steve Butler, Jan 21 2008
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STATUS
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approved
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