A139692 Nonnegative discriminants of the monic general quartic polynomials with integer coefficients.

0, 5, 12, 20, 21, 32, 40, 45, 48, 49, 60, 77, 81, 85, 96, 104, 112, 117, 125, 140, 144, 148, 165, 169, 189, 192, 216, 221, 224, 229, 252, 256, 257, 260, 272, 285, 288, 320, 321, 333, 357, 361, 392, 400, 404, 432, 437, 468, 469, 473, 480, 488, 500, 512, 525, 528, 533, 544, 549

Offset

1,2

Comments

Available discriminants of the general normalized quartic polynomial x^4+c*x^3+d*x^2+e*x+f with c,d,e,f>=0

Links

Table of n, a(n) for n=1..59.

Mathematica

aa = {}; b = 1; Do[Print[f]; Do[Do[Do[k = c^2 d^2 e^2 - 4 b d^3 e^2 - 4 c^3 e^3 + 18 b c d e^3 - 27 b^2 e^4 - 4 c^2 d^3 f + 16 b d^4 f + 18 c^3 d e f - 80 b c d^2 e f - 6 b c^2 e^2 f + 144 b^2 d e^2 f - 27 c^4 f^2 + 144 b c^2 d f^2 - 128 b^2 d^2 f^2 - 192 b^2 c e f^2 + 256 b^3 f^3; If[k > 0 && k < 1000, AppendTo[aa, k]], {c, 0, 30}], {d, 0, 30}], {e, 0, 30}], {f, 1, 30}]; Union[aa]]

Crossrefs

Cf. A014601, A042948, A139691.

Sequence in context: A047704 A043413 A017041 * A099192 A047077 A326663

Adjacent sequences: A139689 A139690 A139691 * A139693 A139694 A139695

Keyword

nonn

Author

Artur Jasinski, Apr 29 2008

Extensions

Edited, and some missing terms inserted, by Robert Israel, May 16 2018

Status

approved