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%I #2 Mar 30 2012 17:36:44
%S 0,38,384,1614,4592,10506,20828,37358,62132,97574,146308,211418,
%T 296032,403918,538784,704918,906720,1149162,1437036,1776038,2171556,
%U 2629790,3156924,3759698,4444648,5219390,6091008,7067614,8157088,9368178
%N Number of cubic equations ax^3 + bx^2 + cx + d = 0 with integer coefficients |a|,|b|,|c|,|d| <= n, a <> 0, having one real root and two conjugate complex roots.
%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.
%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, A155192.
%K nonn
%O 0,2
%A _Rick L. Shepherd_, Jan 21 2009
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