login
A136781
Number of multiplex juggling sequences of length n, base state <2,2> and hand capacity 2.
2
1, 3, 21, 162, 1305, 10719, 88830, 739179, 6162669, 51425010, 429299217, 3584510631, 29932216686, 249957514899, 2087382613509, 17431787135682, 145573937119305, 1215699423313455, 10152411188679774, 84783702198390651, 708036493717628253, 5912878431088447506
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.
S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, Ann. Combinat. 13 (4) (2010) 412.
FORMULA
G.f.: (x-11*x^2+33*x^3-27*x^4)/(1-14*x+54*x^2-57*x^3).
a(n) = 14*a(n-1)-54*a(n-2)+57*a(n-3) for n>4. - Colin Barker, Aug 31 2016
MATHEMATICA
LinearRecurrence[{14, -54, 57}, {1, 3, 21, 162}, 30] (* Harvey P. Dale, Apr 19 2023 *)
PROG
(PARI) Vec((x-11*x^2+33*x^3-27*x^4)/(1-14*x+54*x^2-57*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 25); Coefficients(R!( (x-11*x^2+33*x^3-27*x^4)/(1-14*x+54*x^2-57*x^3))); // Marius A. Burtea, Jan 13 2020
CROSSREFS
Cf. A136782.
Sequence in context: A358953 A189508 A074570 * A225439 A180400 A166696
KEYWORD
nonn,easy
AUTHOR
Steve Butler, Jan 21 2008
STATUS
approved