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A065177 Table M(n,b) (columns: n >= 1, rows: b >= 0) gives the number of site swap juggling patterns with exact period n, using exactly b balls, where cyclic shifts are not counted as distinct. 5
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 3, 6, 3, 1, 0, 6, 15, 12, 4, 1, 0, 9, 42, 42, 20, 5, 1, 0, 18, 107, 156, 90, 30, 6, 1, 0, 30, 294, 554, 420, 165, 42, 7, 1, 0, 56, 780, 2028, 1910, 930, 273, 56, 8, 1, 0, 99, 2128, 7350, 8820, 5155, 1806, 420, 72, 9, 1, 0, 186, 5781, 26936 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

Juggling Information Service, Site Swap FAQs

EXAMPLE

Upper left corner starts as:

1, 0,  0,  0,   0, ...

1, 1,  2,  3,   6, ...

1, 2,  6, 15,  42, ...

1, 3, 12, 42, 156, ...

1, 4, 20, 90, 420, ...

...

MAPLE

[seq(DistSS_table(j), j=0..119)]; DistSS_table := (n) -> DistSS((((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)+1, (n-((trinv(n)*(trinv(n)-1))/2)));

with(numtheory); DistSS := proc(n, b) local d, s; s := 0; for d in divisors(n) do s := s+mobius(n/d)*((b+1)^d - b^d); od; RETURN(s/n); end;

MATHEMATICA

trinv[n_] := Floor[(1 + Sqrt[8 n + 1])/2];

DistSS[n_, b_] := DivisorSum[n, MoebiusMu[n/#]*((b + 1)^# - b^#)&] /n;

a[n_] := DistSS[(((trinv[n] - 1)*(((1/2)*trinv[n]) + 1)) - n) + 1, (n - ((trinv[n]*(trinv[n] - 1))/2))];

Table[a[n], {n, 0, 119}] (* Jean-Fran├žois Alcover, Mar 06 2016, adapted from Maple *)

CROSSREFS

Row 1: A059966, row 2: A065178, row 3: A065179, row 4: A065180. Column 1: A002378, column 2: A059270. Cf. also A065167. trinv given at A054425.

Sequence in context: A155161 A185937 A292086 * A064044 A213980 A144912

Adjacent sequences:  A065174 A065175 A065176 * A065178 A065179 A065180

KEYWORD

nonn,tabl,changed

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified December 14 21:16 EST 2017. Contains 296020 sequences.