|
| |
|
|
A113279
|
|
Triangle T(n,k) of coefficients of r_1^n+r_2^n in terms of p and q, where r_1,r_2 are the roots of x^2+px+q=0.
|
|
1
|
|
|
|
2, -1, 1, -2, -1, 3, 1, -4, 2, -1, 5, -5, 1, -6, 9, -2, -1, 7, -14, 7, 1, -8, 20, -16, 2, -1, 9, -27, 30, -9, 1, -10, 35, -50, 25, -2, -1, 11, -44, 77, -55, 11, 1, -12, 54, -112, 105, -36, 2, -1, 13, -65, 156, -182, 91, -13, 1, -14, 77, -210, 294, -196, 49, -2, -1, 15, -90, 275, -450, 378, -140, 15
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
The triangle begins: 2 .-1 1..-2 .-1..3 1..-4.2
|
|
|
REFERENCES
|
M. Herkenhoff Konersmann, Sprokkel XXXI: x_1^n+x_2^n, Nieuw Tijdschr. Wisk, 42 (1954-55) 180.
|
|
|
LINKS
|
Table of n, a(n) for n=0..71.
|
|
|
FORMULA
|
T(n, k)=(-1)^(n+k)*A034807(n, k)
|
|
|
EXAMPLE
|
x_1^5+x_2^5 = -p^5 + 5p^3q - 5pq^2, so row 5 reads -1, 5, -5.
|
|
|
CROSSREFS
|
Sequence in context: A050221 A213235 * A213234 A034807 A182961 A135062
Adjacent sequences: A113276 A113277 A113278 * A113280 A113281 A113282
|
|
|
KEYWORD
|
easy,sign,tabf
|
|
|
AUTHOR
|
Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 22 2005
|
|
|
STATUS
|
approved
|
| |
|
|
