|
| |
|
|
A231188
|
|
Coefficient table for the minimal polynomials of 2*sin(2*Pi/n). Rising powers of x.
|
|
5
|
|
|
|
0, 1, 0, 1, -3, 0, 1, -2, 1, 5, 0, -5, 0, 1, -3, 0, 1, -7, 0, 14, 0, -7, 0, 1, -2, 0, 1, -3, 0, 9, 0, -6, 0, 1, 5, 0, -5, 0, 1, -11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1, -1, 1, 13, 0, -91, 0, 182, 0, -156, 0, 65, 0, -13, 0, 1, -7, 0, 14, 0, -7, 0, 1, 1, 0, -8, 0, 14, 0, -7, 0, 1, 2, 0, -4, 0, 1, 17, 0, -204, 0, 714, 0, -1122, 0, 935, 0, -442, 0, 119, 0, -17, 0, 1, -3, 0, 9, 0, -6, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
The length of row n is deg(n) + 1 = A093819(n) + 1, that is 2, 2, 3, 2, 5, 3, 7, 3, 7, 5, 11, 2, 13, 7, 9, 5, 17,...
See A181871 for the coefficient table for the integer but non-monic minimal polynomials of sin(2*Pi/n), n>=1, called there pi(n, x). The present minimal polynomials of 2*sin(2*Pi/n) are integer and monic, and they are given by
MP2sin2(n, x) = pi(n, x/2).
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n,m) = [x^m] MP2sin2(n, x), n>=1, m = 0, 1, ..., A093819(n), with the minimal polynomials of 2*sin(2*Pi/n), given above in a comment in terms of the ones for sin(2*Pi/n).
|
|
|
EXAMPLE
|
The table a(n,m) starts:
---------------------------------------------------------------------------------
n\m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
1: 0 1
2: 0 1
3: -3 0 1
4: -2 1
5: 5 0 -5 0 1
6: -3 0 1
7: -7 0 14 0 -7 0 1
8: -2 0 1
9: -3 0 9 0 -6 0 1
10: 5 0 -5 0 1
11: -11 0 55 0 -77 0 44 0 -11 0 1
12: -1 1
13: 13 0 -91 0 182 0 -156 0 65 0 -13 0 1
14: -7 0 14 0 -7 0 1
15: 1 0 -8 0 14 0 -7 0 1
16: 2 0 -4 0 1
17: 17 0 -204 0 714 0 -1122 0 935 0 -442 0 119 0 -17 0 1
...
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign,tabf
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
