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A113975
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Devil's Farey: coefficient expansion of a quadratic over quadratic that has 123 roots and a Farey p[1/2]=1 ( correction).
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0
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2, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| I call it the devil's Farey because of the 6,6,6 structure. I was trying to get an integer root quadratic over quadratic that had the Farey conditions: p[1/2]=1;p[0]=0;p[1]=0
The function has the characteristic Farey shape: fa[x_] := 1/p[x] /; 0 <= x <= 1/2 fa[x_] := p[x] /; 1/2 < x <= 1.
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FORMULA
| b(n)= coefficient expansion of 1 + 2/x - 6/(1 - x) a(n) = b(n)
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MATHEMATICA
| a = 1; b = 2; c = 3; d = 3; e = 0; f = -1 p[x_] = FullSimplify[ExpandAll[(x - a)*(x - b)*(x - c)/((x - d)*(x - e)*(x -f))]] a = Abs[ReplacePart[Table[Abs[Coefficient[Series[p[x], {x, 0, 30}], x^n]], {n, -1, 30}], -5, 2]]
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CROSSREFS
| Cf. A113923.
Sequence in context: A155947 A008294 A019694 * A035585 A159076 A146099
Adjacent sequences: A113972 A113973 A113974 * A113976 A113977 A113978
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2006
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