|
Search: id:A114798
|
|
|
| A114798 |
|
Cubic polynomial coefficients such that an elliptical term is zero. |
|
+0
1
|
|
| 3, 2, 12, 16, 27, 54, 48, 128, 75, 250, 108, 432, 147, 686, 192, 1024, 243, 1458, 300, 2000, 363, 2662, 432, 3456, 507, 4394, 588, 5488, 675, 6750, 768, 8192, 867, 9826, 972, 11664, 1083, 13718, 1200, 16000, 1323, 18522, 1452, 21296, 1587, 24334, 1728
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
I had noticed that the elliptical term: j=g2[n]^3/(g2[n]^2-27*g3[n]^2) was singular for a kind of polynomial with three real roots: (x+n)^2*(x-2*n) This table gives all zeros: Table[((4*a[[2*n + 1]])^3 - 27*(4*a[[2*n + 2]])^2)/(4*a[[2*n + 1]])^3, {n, 0, 49}]
|
|
FORMULA
|
w^2=4*z^3-g2[n]*z-g3[n] a(n) = {g2[n],g3[n]}/4
|
|
EXAMPLE
|
x^3-3*x-2
x^3-12*x-16
x^3-27*x-54
|
|
MATHEMATICA
|
a = Flatten[Table[Abs[Coefficient[Expand[(x + n)^2*(x - 2*n)], x, 1 - m]], {n, 1, 50}, {m, 0, 1}]]
|
|
CROSSREFS
|
Sequence in context: A129925 A057779 A005220 this_sequence A113205 A136657 A006774
Adjacent sequences: A114795 A114796 A114797 this_sequence A114799 A114800 A114801
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger Bagula (rlbagulatftn(AT)yahoo.com), Feb 18 2006
|
|
|
Search completed in 0.002 seconds
|
