A065179 Number of site swap patterns with 3 balls and exact period n.

1, 3, 12, 42, 156, 554, 2028, 7350, 26936, 98874, 365196, 1353520, 5039580, 18831306, 70626140, 265741350, 1002984060, 3796211692, 14406086604, 54801192684, 208932673508, 798218225802, 3055417434732, 11716355452900

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 three-ball cascade), three period two (42/24, 51/15 = three-ball shower and 60/06) and twelve period three 3-ball 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^d-3^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] (* Jean-François 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