A181876 Denominators of coefficient array of minimal polynomials of cos(2*Pi/n). Rising powers in x.

1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 2, 1, 8, 2, 2, 1, 2, 1, 1, 8, 4, 1, 1, 4, 2, 1, 32, 16, 8, 1, 2, 1, 4, 1, 1, 64, 32, 8, 2, 4, 2, 1, 8, 2, 2, 1, 16, 2, 1, 2, 1, 8, 1, 1, 1, 1, 256, 32, 32, 16, 16, 4, 4, 2, 1, 8, 4, 1, 1, 512, 256, 64, 16, 32, 16, 8, 1, 2, 1, 16, 1, 4, 1, 1, 64, 4, 2, 4, 2, 2

Offset: 1

Author

Wolfdieter Lang, Jan 08 2011

Keywords

• nonn
• easy
• tabf

Comments

The corresponding numerator array is A181875(n,m).

The sequence of row lengths is d(n)+1, with d(n):=A023022(n), n >= 2, and d(1):=1: [2, 2, 2, 2, 3, 2, 4, 3, 4, 3, 6, 3, 7, 4, 5, 5, 9, 4, 10, 5, 7, ...].

For details on the monic, minimal degree rational polynomial with one of its zeros cos(2*Pi/n), n >= 1 (so-called minimal polynomial of cos(2*Pi/n)), see the array A181875(n,m) where also references are found.

Examples

			[1,1], [1,1], [2,1], [1,1], [4,2,1], [2,1], [8,2,2,1], [2,1,1], [8,4,1,1], [4,2,1], ...
		

References

• See A181875.

Links

• See A181875.

Crossrefs

Cf. A023022, A181875, A181877, A183918.

Programs

Mathematica

ro[n_] := Denominator[ cc = CoefficientList[ MinimalPolynomial[ Cos[2*Pi/n], x], x] ; cc/Last[cc]]; Flatten[Table[ro[n], {n, 1, 21}]] (* Jean-François Alcover, Sep 27 2011 *)

Formula

a(n,m) = denominator([x^m]Psi(n,x)), with the minimal polynomial Psi(n,x) of cos(2*Pi/n), n >= 1. See A181875 for details and references.