login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A231146 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. 1

%I

%S 1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1,0,-1,0,1,1,-1,-3,2,5,-2,-3,1,1,1,1,-1,

%T -1,1,1,-1,-5,4,12,-8,-15,8,12,-4,-5,1,1,1,0,-4,0,7,0,-4,0,1,1,0,-6,

%U -1,15,3,-19,-3,15,1,-6,0,1,1,1,-3,-2,5,2,-3,-1,1

%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 .. -1 ... 1 ... 1

%e 1 .... 0 .. -1 ... 0 ... 1

%e 1 ... -1 .. -3 ... 2 ... 5 ... -2 ... -3 ... 1 ... 1

%e First 4 polynomials: 1, -1 - x + x^2, -1 + x + x^2, 1 - x - 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. A230003.

%K tabf,sign,easy

%O 0,20

%A _Clark Kimberling_, Nov 07 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 03:10 EDT 2021. Contains 348073 sequences. (Running on oeis4.)