

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
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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 threeball cascade), three period two (42/24, 51/15 = threeball shower and 60/06) and twelve period three 3ball 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^d3^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] (* JeanFrançois 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



