Table of triples (a,b,c) of quadratic forms having the number of discriminants given in A107628.
1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 3, 1, 0, 3, 1, 1, 4, 2, 1, 2, 1, 0, 4, 1, 1, 5, 1, 0, 5, 2, 2, 3, 1, 1, 6, 2, 1, 3, 1, 0, 6, 2, 0, 3, 1, 1, 7, 1, 0, 7, 1, 1, 8, 2, 1, 4, 1, 0, 8, 3, 2, 3, 1, 1, 9, 3, 1, 3, 1, 0, 9, 2, 2, 5, 1, 1, 10, 2, 1, 5, 3, 3, 4
1
See S000138 for this sequence with the discriminant prepended.
T. D. Noe, Plot of 1000 triples
T. D. Noe, Table of 1000 triples
Example: the first triple is for x^2 + x*y + y^2. The second is x^2 + y^2.
(Mma) dLim = 100; cnt = 0; dLst = {}; nn = Ceiling[dLim/4]; Do[d = b^2 - 4 a c; If[GCD[a, b, c] == 1 && 0 < -d < dLim, cnt++; AppendTo[dLst, {-d, a, b, c}]], {b, 0, nn}, {a, b, nn}, {c, a, nn}]; dLst = Sort[dLst]; Flatten[Rest /@ dLst]
nonn,tabl
T. D. Noe, Jul 14 2014