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A357301 a(n) is the number of distinct radii of circles passing through at least three points in a square grid of n X n points. 1
0, 1, 7, 19, 48, 112, 212, 383, 641, 988, 1523, 2250, 3103, 4364, 5831, 7696, 9985, 12945, 16164, 20246, 24946, 30145, 36385, 43839, 51752, 61610, 72475, 84273, 97231, 112733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Proposed by Ed Pegg Jr in Mathematics StackExchange question 273348, where terms up to 212 were given, see link.
LINKS
Mathematics StackExchange, Number of circles in configuration, comment by Ed Pegg, Jan 09, 2013.
EXAMPLE
a(2) = 1: only one possible circle with squared radius 1/2;
a(3) = 7: squared radii of possible circles are {1, 2, 1/2, 5/2, 5/4, 25/16, 25/18}.
PROG
(PARI) \\ Function r2 determined using Mathematica
\\ (ArcLength [CircleThrough[{{x1, y1}, {x2, y2}, {x3, y3}}]]/(2*Pi))^2
radii(n) = {my (R=List(), r2(x1, y1, x2, y2, x3, y3) = ((x3 + (x2^2*y1 - x3^2*y1 - x1^2*y2 + x3^2*y2 - y1^2*y2 + y1*y2^2 + x1^2*y3 - x2^2*y3 + y1^2*y3 - y2^2*y3 - y1*y3^2 + y2*y3^2)/(2*(-x2*y1 + x3*y1 + x1*y2 - x3*y2 - x1*y3 + x2*y3)))^2 + (y3 - (-2*(x2 - x3)*(x1^2 - x3^2 + y1^2 - y3^2) + 2*(x1 - x3)*(x2^2 - x3^2 + y2^2 - y3^2))/(-4*x2*y1 + 4*x3*y1 + 4*x1*y2 - 4*x3*y2 - 4*x1*y3 + 4*x2*y3))^2)); 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); listput (R, r2(x1, y1, x2, y2, x3, y3)))))))); Set(R)};
for (k=1, 15, print1(#radii(k), ", "))
CROSSREFS
Sequence in context: A000491 A097039 A067651 * A090025 A348472 A003232
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner, Sep 23 2022, following a suggestion by Ed Pegg Jr, Jan 09 2013
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)