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!)
A136783 Number of multiplex juggling sequences of length n, base state <3> and hand capacity 3. 2
1, 4, 20, 112, 660, 3976, 24180, 147648, 903140, 5528504, 33853220, 207325392, 1269787060, 7777149416, 47633751380, 291750220768, 1786933908740, 10944758154264, 67035370422020, 410583912229872, 2514779283989460, 15402734618128456, 94339983758166580 (list; graph; refs; listen; history; text; internal format)
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-6*x^2+7*x^3)/(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>3. - Colin Barker, Aug 31 2016

EXAMPLE

a(2)=4 since <3> -> <3> -> <3>; <3> -> <2,1> -> <3>; <3> -> <1,2> -> <3> and <3> -> <0,3> -> <3> are the four possibilities.

PROG

(PARI) Vec((x-6*x^2+7*x^3)/(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-6*x^2+7*x^3)/(1-10*x+27*x^2-20*x^3))); // Marius A. Burtea, Jan 13 2020

CROSSREFS

Cf. A136784.

Sequence in context: A153299 A239643 A081335 * A227726 A080609 A003645

Adjacent sequences:  A136780 A136781 A136782 * A136784 A136785 A136786

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 February 22 04:58 EST 2020. Contains 332115 sequences. (Running on oeis4.)