A113975 Devil's Farey: coefficient expansion of a quadratic over quadratic that has 123 roots and a Farey p[1/2]=1 ( correction).

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..31.

Formula

b(n)= coefficient expansion of 1 + 2/x - 6/(1 - x) a(n) = b(n)

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]]

Crossrefs

Cf. A113923.

Sequence in context: A008294 A019694 A233588 * A035585 A239868 A159076

Adjacent sequences: A113972 A113973 A113974 * A113976 A113977 A113978

Keyword

nonn,uned

Author

Roger L. Bagula, Jan 31 2006

Status

approved