A136778 Number of primitive multiplex juggling sequences of length n, base state <2,1> and hand capacity 2.

1, 3, 15, 75, 381, 1947, 9975, 51159, 262497, 1347123, 6913911, 35485779, 182133885, 934823451, 4798101855, 24626900271, 126400914849, 648769995939, 3329901037119, 17091174551835, 87722802540957, 450249343708827, 2310966659437671, 11861354115061383

Offset: 1

Author

Steve Butler, Jan 21 2008

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597 [math.CO], 2008.
• Index entries for linear recurrences with constant coefficients, signature (7,-9,-3).

Crossrefs

Cf. A136777.

Programs

PARI

Vec((x-4*x^2+3*x^3)/(1-7*x+9*x^2+3*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016

Formula

G.f.: (x-4*x^2+3*x^3)/(1-7*x+9*x^2+3*x^3).

a(n) = 7*a(n-1)-9*a(n-2)-3*a(n-3) for n>3. - Colin Barker, Aug 31 2016