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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-François 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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