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A136779 Number of multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2. 2
1, 3, 18, 105, 606, 3483, 19986, 114609, 657054, 3766515, 21590418, 123758649, 709393758, 4066287627, 23308182162, 133603718145, 765823377054, 4389738680547, 25162205542674, 144231041494281, 826739659899486, 4738913739770235, 27163694339468562 (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 (8,-13).

FORMULA

G.f.: (x-5*x^2+7*x^3)/(1-8*x+13*x^2).

From Colin Barker, Aug 31 2016: (Start)

a(n) = 8*a(n-1)-13*a(n-2) for n>3.

a(n) = ((9-14*sqrt(3))*(4-sqrt(3))^n+(4+sqrt(3))^n*(9+14*sqrt(3)))/338 for n>1.

(End)

PROG

(PARI) Vec((x-5*x^2+7*x^3)/(1-8*x+13*x^2) + O(x^30)) \\ Colin Barker, Aug 31 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-5*x^2+7*x^3)/(1-8*x+13*x^2))); // Marius A. Burtea, Jan 13 2020

CROSSREFS

Cf. A136780.

Sequence in context: A009021 A303519 A124408 * A106328 A007277 A025595

Adjacent sequences:  A136776 A136777 A136778 * A136780 A136781 A136782

KEYWORD

nonn,easy

AUTHOR

Steve Butler, Jan 21 2008

STATUS

approved

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Last modified March 28 15:03 EDT 2020. Contains 333089 sequences. (Running on oeis4.)