A113975 - OEIS

%I #2 Mar 30 2012 17:34:20

%S 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

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

%C 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

%C The function has the characteristic Farey shape: fa[x_] := 1/p[x] /; 0 <= x <= 1/2 fa[x_] := p[x] /; 1/2 < x <= 1.

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

%t 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]]

%Y Cf. A113923.

%K nonn,uned

%O 0,1

%A _Roger L. Bagula_, Jan 31 2006