A136785 Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 3.

1, 5, 30, 182, 1110, 6786, 41530, 254278, 1557190, 9536994, 58411370, 357758662, 2191219510, 13420938626, 82201632730, 503475374598, 3083728434790, 18887481888354, 115683658636170, 708549144071942, 4339782295309910, 26580669235880066, 162803553266871930

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

Author

Steve Butler, Jan 21 2008

Status

approved