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A065178 Number of site swap patterns with 2 balls and exact period n. 6


%S 1,2,6,15,42,107,294,780,2128,5781,15918,43885,122010,340323,954394,

%T 2685930,7588770,21507696,61144062,174283887,498012094,1426213191,

%U 4092816966,11767176070,33890202192,97761428205,282424564744

%N Number of site swap patterns with 2 balls and exact period n.

%C When interspersed with 0's, exponents in expansion of A065481 as a product zeta(n)^(-a(n)).

%H G. C. Greubel, <a href="/A065178/b065178.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>

%H M. Macauley, <a href="http://www.math.hmc.edu/seniorthesis/archives/2003/mmacaule/mmacaule-2003-thesis.pdf">Braids and Juggling patterns</a>, Thesis (Harvey Mudd College) 2003, eq. (A1)

%H G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]

%F a(n) ~ 3^n/n. - _Vaclav Kotesovec_, Mar 05 2016

%F Inverse Euler transform of A133494. - _Alois P. Heinz_, Jun 23 2018

%e We have one period 1 (2), two period 2 (31/13 and 40/04) and six period three 2-ball siteswaps (312, 330, 411, 420, 501, 600) (The average of the digits is always 2).

%p [seq(DistSS(p,2),p=1..60)];

%p A065178 := proc(n)

%p add( mobius(n/d)*(3^d-2^d),d=numtheory[divisors](n)) /n ;

%p end proc:

%p seq(A065178(n),n=1..30) ; # _R. J. Mathar_, Aug 05 2015

%t a[n_] := DivisorSum[n, MoebiusMu[n/#] * (3^#-2^#)&] / n; Array[a, 30] (* _Jean-Fran├žois Alcover_, Mar 05 2016, after _R. J. Mathar_ *)

%Y Row 2 of A065177. Cf. A065179, A065180, A065481.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 19 2001

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Last modified January 23 01:15 EST 2020. Contains 331166 sequences. (Running on oeis4.)