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%I #9 Apr 15 2016 02:47:18
%S 0,10,32,70,132,198,272,370,504,646,780,934,1152,1330,1520,1734,2036,
%T 2270,2560,2818,3184,3494,3788,4110,4584,4970,5328,5782,6284,6686,
%U 7128,7554,8192
%N Number of cubic equations ax^3 + bx^2 + cx + d = 0 with integer coefficients |a|,|b|,|c|,|d| <= n, a <> 0, having three real roots, of which at least two are equal.
%C Clearly each term is even as ax^3 + bx^2 + cx + d = 0 and -ax^3 - bx^2 - cx - d = 0 have the same roots.
%C The variable D in the PARI program below is the discriminant of the reduced form y^3 + py + q = 0.
%D Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & Co., NY, pages 318-9.
%H Gheorghe Coserea, <a href="/A155192/b155192.txt">Table of n, a(n) for n = 0..512</a>
%o (PARI) {for(n=0, 32, c=0; forvec(xx=[[ -n,n],[ -n,n],[ -n,n],[ -n,n]],
%o if(xx[1]==0, next, z=Pol(xx); x=y-xx[2]/(3*xx[1]);
%o zz=eval(z); if(polcoeff(zz,3)<>1, zz=zz/polcoeff(zz,3));
%o p=polcoeff(zz,1); q=polcoeff(zz,0); D=(q/2)^2+(p/3)^3;
%o if(D==0, c++))); print1(c,","))}
%Y Cf. A155191, A155193.
%K nonn
%O 0,2
%A _Rick L. Shepherd_, Jan 21 2009
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