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Search: id:A065177
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| A065177 |
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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. |
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6
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| 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; listen)
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OFFSET
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0,8
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LINKS
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Joe Buhler and Ron Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
Juggling Information Service, Site Swap FAQs
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MAPLE
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[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;
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CROSSREFS
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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: A063250 A107424 A155161 this_sequence A064044 A144912 A145337
Adjacent sequences: A065174 A065175 A065176 this_sequence A065178 A065179 A065180
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen Oct 19 2001
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