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A139692 Nonnegative discriminants of the monic general quartic polynomials with integer coefficients. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)