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 A355884 Number of circles in an n X n grid passing through at least three points. 1
 0, 0, 1, 34, 223, 997, 3402, 9141, 21665, 46390, 90874, 167539, 293443, 487082, 781537, 1209469, 1816528, 2661113, 3822203, 5369662, 7420495, 10086360, 13494376 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A192493, A192494, A357301. Sequence in context: A058581 A050263 A020869 * A055716 A233300 A281052 Adjacent sequences: A355881 A355882 A355883 * A355885 A355886 A355887 KEYWORD nonn,hard,more AUTHOR Sharvil Kesarwani, Jul 20 2022 STATUS approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)