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Search: id:A139692
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| A139692 |
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Discriminants of the normalized general quartic polynomials with nonnegative coefficients. |
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1
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| 0, 5, 12, 20, 21, 32, 40, 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, 500, 512, 528, 544, 549
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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MAPLE
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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]] (*Artur Jasinski*)
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CROSSREFS
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Cf. A014601, A042948, A139691.
Adjacent sequences: A139689 A139690 A139691 this_sequence A139693 A139694 A139695
Sequence in context: A047704 A043413 A017041 this_sequence A099192 A047077 A086570
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Apr 29 2008
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