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A139691 Discriminants of the normalized general quintic polynomials with nonnegative coefficients. 1
0, 12, 40, 48, 49, 69, 84, 92, 93, 117, 124, 125, 128, 132, 144, 161, 176, 184, 189, 217, 229, 240, 245, 256, 257, 272, 312, 320, 324, 332, 333, 340, 348, 392, 400, 432, 448, 456, 472, 512, 549, 588, 592, 605, 609, 688, 697, 708, 725, 761, 804, 832, 836, 837 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Possible discriminants of the general normalized quintic polynomial x^5+b*x^4+c*x^3+d*x^2+e*x+f with b,c,d,e,f>=0

REFERENCES

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257.  Mathematical Reviews, MR2312537.  Zentralblatt MATH, Zbl 1133.11012.

LINKS

Table of n, a(n) for n=1..54.

MATHEMATICA

aa = {}; a = 1; Do[Print[f]; Do[Do[Do[Do[k = b^2 c^2 d^2 e^2 - 4 a c^3 d^2 e^2 - 4 b^3 d^3 e^2 + 18 a b c d^3 e^2 - 27 a^2 d^4 e^2 - 4 b^2 c^3 e^3 + 16 a c^4 e^3 + 18 b^3 c d e^3 - 80 a b c^2 d e^3 - 6 a b^2 d^2 e^3 + 144 a^2 c d^2 e^3 - 27 b^4 e^4 + 144 a b^2 c e^4 - 128 a^2 c^2 e^4 - 192 a^2 b d e^4 + 256 a^3 e^5 - 4 b^2 c^2 d^3 f + 16 a c^3 d^3 f + 16 b^3 d^4 f - 72 a b c d^4 f + 108 a^2 d^5 f + 18 b^2 c^3 d e f - 72 a c^4 d e f - 80 b^3 c d^2 e f + 356 a b c^2 d^2 e f + 24 a b^2 d^3 e f - 630 a^2 c d^3 e f - 6 b^3 c^2 e^2 f + 24 a b c^3 e^2 f + 144 b^4 d e^2 f - 746 a b^2 c d e^2 f + 560 a^2 c^2 d e^2 f + 1020 a^2 b d^2 e^2 f - 36 a b^3 e^3 f + 160 a^2 b c e^3 f - 1600 a^3 d e^3 f - 27 b^2 c^4 f^2 + 108 a c^5 f^2 + 144 b^3 c^2 d f^2 - 630 a b c^3 d f^2 - 128 b^4 d^2 f^2 + 560 a b^2 c d^2 f^2 + 825 a^2 c^2 d^2 f^2 - 900 a^2 b d^3 f^2 - 192 b^4 c e f^2 + 1020 a b^2 c^2 e f^2 - 900 a^2 c^3 e f^2 + 160 a b^3 d e f^2 - 2050 a^2 b c d e f^2 + 2250 a^3 d^2 e f^2 - 50 a^2 b^2 e^2 f^2 + 2000 a^3 c e^2 f^2 + 256 b^5 f^3 - 1600 a b^3 c f^3 + 2250 a^2 b c^2 f^3 + 2000 a^2 b^2 d f^3 - 3750 a^3 c d f^3 - 2500 a^3 b e f^3 + 3 125 a^4 f^4; If[k > 0 && k < 1000, AppendTo[aa, k]], {b, 0, 30}], {c, 0, 30}], {d, 0, 30}], {e, 0, 30}], {f, 0, 30}]; Union[aa] (*Artur Jasinski*)

CROSSREFS

Cf. A014601, A042948.

Sequence in context: A236267 A119094 A226348 * A292544 A114815 A175583

Adjacent sequences:  A139688 A139689 A139690 * A139692 A139693 A139694

KEYWORD

nonn

AUTHOR

Artur Jasinski, Apr 29 2008

STATUS

approved

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Last modified September 16 10:36 EDT 2019. Contains 327094 sequences. (Running on oeis4.)