OFFSET
0,2
COMMENTS
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.
The variable D in the PARI program below is the discriminant of the reduced form y^3 + py + q = 0.
REFERENCES
Jan Gullberg, Mathematics, From the Birth of Numbers, W. W. Norton & Co., NY, pages 318-9.
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..128
PROG
(PARI) {for(n=0, 32, c=0; forvec(xx=[[ -n, n], [ -n, n], [ -n, n], [ -n, n]],
if(xx[1]==0, next, z=Pol(xx); x=y-xx[2]/(3*xx[1]);
zz=eval(z); if(polcoeff(zz, 3)<>1, zz=zz/polcoeff(zz, 3));
p=polcoeff(zz, 1); q=polcoeff(zz, 0); D=(q/2)^2+(p/3)^3;
if(D<0, c++))); print1(c, ", "))}
(PARI)
Delta(a, b, c, d) = b^2*c^2 - 4*a*c^3 - 4*b^3*d - 27*a^2*d^2 + 18*a*b*c*d;
seq(n) = {
my(a = vector(n));
forvec(v=[[1, n], [-n, n], [-n, n], [-n, n]],
if (Delta(v[1], v[2], v[3], v[4]) > 0, a[vecmax(abs(v))]++));
for (i = 2, #a, a[i] += a[i-1]);
return(concat(0, 2*a));
};
seq(31) \\ Gheorghe Coserea, Apr 09 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Jan 21 2009
STATUS
approved