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A136785 Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 3. 2
1, 5, 30, 182, 1110, 6786, 41530, 254278, 1557190, 9536994, 58411370, 357758662, 2191219510, 13420938626, 82201632730, 503475374598, 3083728434790, 18887481888354, 115683658636170, 708549144071942, 4339782295309910, 26580669235880066, 162803553266871930 (list; graph; refs; listen; history; text; internal format)
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-5*x^2+7*x^3-3*x^4)/(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>4. - Colin Barker, Aug 31 2016

MATHEMATICA

LinearRecurrence[{10, -27, 20}, {1, 5, 30, 182}, 30] (* Harvey P. Dale, Jan 08 2020 *)

PROG

(PARI) Vec((x-5*x^2+7*x^3-3*x^4)/(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-5*x^2+7*x^3-3*x^4)/(1-10*x+27*x^2-20*x^3))); // Marius A. Burtea, Jan 13 2020

CROSSREFS

Cf. A136786.

Sequence in context: A094167 A051738 A052934 * A227383 A155195 A147837

Adjacent sequences:  A136782 A136783 A136784 * A136786 A136787 A136788

KEYWORD

nonn,easy,changed

AUTHOR

Steve Butler, Jan 21 2008

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)