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

1,5

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.

References

See A181875.

Links

Table of n, a(n) for n=1..91.

See A181875.

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.

Example

[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], ...

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 *)

Crossrefs

Cf. A023022, A181875, A181877, A183918.

Sequence in context: A235388 A294897 A252733 * A131505 A100092 A131508

Adjacent sequences: A181873 A181874 A181875 * A181877 A181878 A181879

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang, Jan 08 2011

Status

approved