login
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
OFFSET
1,2
LINKS
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.
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
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 21 2008
STATUS
approved