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Number of site swap patterns with 4 balls and exact period n.
5

%I #12 Dec 11 2017 02:44:43

%S 1,4,20,90,420,1910,8820,40590,187880,871494,4057620,18945960,

%T 88738020,416787030,1962922276,9268287390,43868210820,208109782580,

%U 989400443220,4713395564772,22497100553820,107572434560790,515241748300020

%N Number of site swap patterns with 4 balls and exact period n.

%H G. C. Greubel, <a href="/A065180/b065180.txt">Table of n, a(n) for n = 1..1000</a>

%H Juggling Information Service, <a href="http://www.juggling.org/bin/mfs/JIS/help/siteswap/">Site Swap FAQs</a>

%p [seq(DistSS(p,4),p=1..60)];

%p A065180 := proc(n)

%p add( mobius(n/d)*(5^d-4^d),d=numtheory[divisors](n)) /n ;

%p end proc:

%p seq(A065180(n),n=1..30) ; # _R. J. Mathar_, Aug 05 2015

%t a[n_] := DivisorSum[n, MoebiusMu[n/#]*(5^# - 4^#)&]/n; Array[a, 25] (* _Jean-François Alcover_, Mar 06 2016 *)

%Y Row 4 of A065177. Cf. A065178, A065179.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 19 2001