|
%I #4 Nov 09 2013 21:44:23
%S 1,1,-1,1,1,1,1,1,1,3,1,1,1,0,3,0,1,1,1,5,4,9,4,5,1,1,1,-1,3,-1,1,1,1,
%T 7,6,20,14,29,14,20,6,7,1,1,1,0,4,0,7,0,4,0,1,1,0,6,1,15,3,21,3,15,1,
%U 6,0,1,1,-1,5,-4,9,-4,5,-1,1,1,1,11,10,54
%N Array of coefficients of numerator polynomials of the rational function p(n, x + 1/x), where p(n,x) is the n-th cyclotomic polynomial.
%C If r is a zero of p(n,x) then (1/2)(r +- sqrt(r^2 - 4) are zeros of q(n,x).
%e First 6 rows:
%e 1
%e 1 .. - 1 ... 1
%e 1 .... 1 ... 1
%e 1 .... 1 ... 3 ... 1 ... 1
%e 1 .... 0 ... 3 ... 0 ... 1
%e 1 .... 1 ... 5 ... 4 ... 9 ... 4 ... 5 ... 1 ... 1
%e First 4 polynomials: 1, 1 - x + x^2, 1 + x + x^2, 1 + x + 3*x^2 + x^3 + x^4.
%t z = 60; p[n_, x_] := p[x] = Cyclotomic[n, x]; Table[p[n, x], {n, 0, z/4}]; f1[n_, x_] := f1[n, x] = Numerator[Factor[p[n, x] /. x -> x + 1/x]]; Table[Expand[f1[n, x]], {n, 0, z/4}]
%t t = Flatten[Table[CoefficientList[f1[n, x], x], {n, 0, z/4}]]
%Y Cf. A231146.
%K tabf,sign,easy
%O 0,10
%A _Clark Kimberling_, Nov 07 2013
|
