login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065179 Number of site swap patterns with 3 balls and exact period n. 4
1, 3, 12, 42, 156, 554, 2028, 7350, 26936, 98874, 365196, 1353520, 5039580, 18831306, 70626140, 265741350, 1002984060, 3796211692, 14406086604, 54801192684, 208932673508, 798218225802, 3055417434732, 11716355452900 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Juggling Information Service, Site Swap FAQs

M. Macauley, Braids and Juggling patterns, Thesis (Harvey Mudd College) 2003, equation A1.

EXAMPLE

We have one period 1 (3, the three-ball cascade), three period two (42/24, 51/15 = three-ball shower and 60/06) and twelve period three 3-ball siteswaps (423, 441, 450, 522, 531, 603, 612, 630, 711, 720, 801, 900) (The average of digits is always 3).

MAPLE

[seq(DistSS(p, 3), p=1..60)];

A065179 := proc(n)

    add( mobius(n/d)*(4^d-3^d), d=numtheory[divisors](n)) /n ;

end proc:

seq(A065179(n), n=1..30) ; # R. J. Mathar, Aug 05 2015

MATHEMATICA

a[n_] := DivisorSum[n, MoebiusMu[n/#]*(4^# - 3^#)&]/n; Array[a, 25] (* Jean-Fran├žois Alcover, Mar 06 2016 *)

CROSSREFS

Row 3 of A065177. Cf. A065178, A065180.

Sequence in context: A066972 A067819 A094970 * A048121 A191112 A066987

Adjacent sequences:  A065176 A065177 A065178 * A065180 A065181 A065182

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2001

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 December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)