A065180 Number of site swap patterns with 4 balls and exact period n.

1, 4, 20, 90, 420, 1910, 8820, 40590, 187880, 871494, 4057620, 18945960, 88738020, 416787030, 1962922276, 9268287390, 43868210820, 208109782580, 989400443220, 4713395564772, 22497100553820, 107572434560790, 515241748300020

Offset: 1

Author

Antti Karttunen, Oct 19 2001

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Juggling Information Service, Site Swap FAQs

Crossrefs

Row 4 of A065177.

Cf. A008683, A065178, A065179.

Programs

Maple

[seq(DistSS(p,4),p=1..60)];
A065180 := proc(n)
    add( mobius(n/d)*(5^d-4^d),d=numtheory[divisors](n)) /n ;
end proc:
seq(A065180(n),n=1..30) ; # R. J. Mathar, Aug 05 2015

Mathematica

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

Formula

G.f.: Sum_{k>=1} mu(k) * log(1 + x^k/(1 - 5*x^k))/k. - Seiichi Manyama, Apr 14 2025