login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A136784 Number of primitive multiplex juggling sequences of length n, base state <3> and hand capacity 3. 2
1, 3, 13, 67, 369, 2083, 11869, 67875, 388705, 2227267, 12764973, 73165315, 419377873, 2403873891, 13779078781, 78982269667, 452730133185, 2595071559811, 14875080747085, 85264715699139, 488741675881009, 2801492102959267, 16058295037221021, 92046962959297699 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 (9,-21,13).

FORMULA

G.f.: (x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3).

From Colin Barker, Aug 31 2016: (Start)

a(n) = (13+(4-sqrt(3))^n*(4+sqrt(3))-(-4+sqrt(3))*(4+sqrt(3))^n)/39.

a(n) = 9*a(n-1)-21*a(n-2)+13*a(n-3) for n>3.

(End)

EXAMPLE

a(2)=3 since <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the three possibilities.

PROG

(PARI) Vec((x-6*x^2+7*x^3)/(1-9*x+21*x^2-13*x^3) + O(x^30)) \\ Colin Barker, Aug 31 2016

CROSSREFS

Cf. A136783.

Sequence in context: A302303 A201713 A298611 * A284717 A027277 A242798

Adjacent sequences:  A136781 A136782 A136783 * A136785 A136786 A136787

KEYWORD

nonn,easy

AUTHOR

Steve Butler, Jan 21 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)