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A065178 Number of site swap patterns with 2 balls and exact period n. 6
1, 2, 6, 15, 42, 107, 294, 780, 2128, 5781, 15918, 43885, 122010, 340323, 954394, 2685930, 7588770, 21507696, 61144062, 174283887, 498012094, 1426213191, 4092816966, 11767176070, 33890202192, 97761428205, 282424564744 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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, eq. (A1)

G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]

FORMULA

a(n) ~ 3^n/n. - Vaclav Kotesovec, Mar 05 2016

Inverse Euler transform of A133494. - Alois P. Heinz, Jun 23 2018

EXAMPLE

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).

MAPLE

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

A065178 := proc(n)

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

end proc:

seq(A065178(n), n=1..30) ; # R. J. Mathar, Aug 05 2015

MATHEMATICA

a[n_] := DivisorSum[n, MoebiusMu[n/#] * (3^#-2^#)&] / n; Array[a, 30] (* Jean-Fran├žois Alcover, Mar 05 2016, after R. J. Mathar *)

CROSSREFS

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

Sequence in context: A236110 A280782 A307308 * A178936 A221744 A338861

Adjacent sequences:  A065175 A065176 A065177 * A065179 A065180 A065181

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified April 20 11:52 EDT 2021. Contains 343135 sequences. (Running on oeis4.)