A181873 - OEIS

%I #19 Feb 18 2019 06:13:17

%S 1,1,1,1,4,1,1,1,1,16,1,4,1,1,4,1,1,64,1,8,1,4,1,1,2,1,1,64,1,16,1,2,

%T 1,1,16,1,4,1,1,1024,1,256,1,64,1,4,1,4,1,1,2,1,4096,1,1024,1,128,1,

%U 16,1,16,1,4,1,1,64,1,8,1,4,1,1,256,1,8,1,8,1,4,1,1,8,1,1,1,1,65536,1,4096,1,2048,1,512,1,256,1,32,1,16,1,4,1,1,64,1,16,1,2,1,1,262144,1,65536,1,8192,1,1024,1,1024,1,256,1,64,1,2,1,4,1,1,4,2,1,4096,1,64,1,64,1,32,1,4,1,4,1,1,1024,1,256,1,64,1,4,1,4,1,1

%N Denominators of coefficient array for minimal polynomials of sin(2Pi/n). Rising powers of x.

%C The corresponding numerator array is given in A181872(n,m) where details, references, and a W. Lang link are given.

%C The sequence of row lengths of this array is d(n)+1 with d(n)=A093819(n): [2, 2, 3, 4, 5, 3, 7, 3, 7, 5, 11,... ].

%D See A181872.

%H See A181872.

%F a(n,m)=denominator([x^m]Pi(n,x)), n>=1, m=0,1,...,d(n), with the d(n)=A093819(n), and Pi(n,x) the minimal polynomials of sin(2*Pi/n) given in A181872.

%e [1, 1], [1, 1], [4, 1, 1], [1, 1], [16, 1, 4, 1, 1], [4, 1, 1], [64, 1, 8, 1, 4, 1, 1], [2, 1, 1], [64, 1, 16, 1, 2, 1, 1], [16, 1, 4, 1, 1],...

%e The rational coefficients A181872(n,m)/a(n,m) start with:

%e [0, 1], [0, 1], [-3/4, 0, 1], [-1, 1], [5/16, 0, -5/4, 0, 1], [-3/4, 0, 1], [-7/64, 0, 7/8, 0, -7/4, 0, 1], [-1/2, 0, 1], [-3/64, 0, 9/16, 0, -3/2, 0, 1],...

%t p[n_, x_] := MinimalPolynomial[ Sin[2 Pi/n], x]; Flatten[ Denominator[ Table[ coes = CoefficientList[ p[n, x], x]; coes / Last[coes], {n, 1, 22}]]] (* _Jean-François Alcover_, Nov 07 2011 *)

%Y Cf. A181875/A181876 (minimal polynomials of cos(2Pi/n)).

%Y Cf. A181872.

%K nonn,easy,frac,tabf

%O 1,5

%A _Wolfdieter Lang_, Jan 13 2011