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A139692 Nonnegative discriminants of the monic general quartic polynomials with integer coefficients. 0

%I

%S 0,5,12,20,21,32,40,45,48,49,60,77,81,85,96,104,112,117,125,140,144,

%T 148,165,169,189,192,216,221,224,229,252,256,257,260,272,285,288,320,

%U 321,333,357,361,392,400,404,432,437,468,469,473,480,488,500,512,525,528,533,544,549

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

%C 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

%t 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]]

%Y Cf. A014601, A042948, A139691.

%K nonn

%O 1,2

%A _Artur Jasinski_, Apr 29 2008

%E Edited, and some missing terms inserted, by _Robert Israel_, May 16 2018

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Last modified October 17 19:24 EDT 2019. Contains 328127 sequences. (Running on oeis4.)