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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. 7
 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 FORMULA Row n is the inverse Euler transform of j-> n^(j-1). - Alois P. Heinz, Jun 23 2018 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. Main diagonal gives A306173. 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 AUTHOR Antti Karttunen, Oct 19 2001 STATUS approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)