OFFSET
0,2
EXAMPLE
For n = 1, the a(1) = 3 equations are x^2 - x = 0, x^2 + x = 0, and x^2 - 1 = 0.
For n = 2, the a(2) = 7 equations are the 3 equations listed above and x^2 - 2x = 0, x^2 + 2x = 0, x^2 - x - 2 = 0, and x^2 + x - 2 = 0.
MATHEMATICA
ok[b_, c_] := Block[{d = b^2 - 4 c}, d > 0 && IntegerQ@ Sqrt@ d]; a[n_] := Sum[ Boole@ ok[b, c], {b, -n, n}, {c, -n, n}]; Array[a, 57, 0] (* Giovanni Resta, Jan 28 2020 *)
PROG
(Python 3.7) [sum([1 for b in range(-n, n+1) for c in range(-n, n+1) if b**2-4*c > 0 and int((-b+(b**2-4*c)**0.5)/2) == (-b+(b**2-4*c)**0.5)/2]) for n in range(0, 101)]
(PARI) isok(b, c) = (b^2 > 4*c) && issquare(b^2-4*c);
a(n) = sum(b=-n, n, sum(c=-n, n, isok(b, c))); \\ Michel Marcus, Jan 28 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Piperski, Jan 25 2020
EXTENSIONS
a(0)=0 prepended by Michel Marcus, Jan 30 2020
STATUS
approved