OFFSET
0,4
LINKS
C. Lin, Number of circles in configuration, Mathematics Stack Exchange, 2013.
PROG
(PARI) \\ after user joriki's Java code at Mathematics Stack Exchange link
circles(n) = {
my(C = List());
for (x1 = 1, n,
for (y1 = 1, n,
for (x2 = 1, x1,
for (y2 = 1, n,
for (x3 = 1, x2,
for (y3 = 1, n,
my( ax2 = 2 * (x2 - x1),
ay2 = 2 * (y2 - y1),
ax3 = 2 * (x3 - x1),
ay3 = 2 * (y3 - y1),
den = ax2 * ay3 - ax3 * ay2
);
if (den == 0, next);
my( b2 = x2^2 + y2^2 - x1^2 - y1^2,
b3 = x3^2 + y3^2 - x1^2 - y1^2,
x = b2 * ay3 - b3 * ay2,
y = ax2 * b3 - ax3 * b2,
gc = gcd(gcd(x, y), den)
);
if (den < 0, gc = -gc);
x /= gc; y /= gc; den /= gc;
my( dx = x - den * x1,
dy = y - den * y1,
s = dx^2 + dy^2
);
listput(C, [x, y, s, den])
))))));
Set(C)
};
for (k = 0, 10, print1(#circles(k), ", ")) \\ Hugo Pfoertner, Sep 22 2022
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Sharvil Kesarwani, Jul 20 2022
STATUS
approved