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%I #22 Sep 27 2023 14:57:39
%S 5,26,79,185,366,653,1077,1678,2494,3571,4959,6718,8889,11541,14740,
%T 18553,23027,28278,34351,41352,49356,58454,68732,80330,93304,107757,
%U 123815,141605,161211,182795,206393,232190,260331,290907,324090,360080,398856,440655,485655
%N Number of distinct circles that can be constructed from an n X n square grid of points when each pair of points is connected by a circle and the points lie at the ends of a diameter of the circle.
%C A circle is constructed for every pair of points on the n X n grid, the points lying at the ends of a diameter of the circle.
%C No formula for a(n) is known.
%C See A360351 and A360352 for images of the resulting vertices and regions.
%H N. J. A. Sloane, New Gilbreath Conjectures, Sum and Erase, Dissecting Polygons, and Other New Sequences, Doron Zeilberger's Exper. Math. Seminar, Rutgers, Sep 14 2023: <a href="https://vimeo.com/866583736?share=copy">Video</a>, <a href="http://neilsloane.com/doc/EMSep2023.pdf">Slides</a>, <a href="http://neilsloane.com/doc/EMSep2023.Updates.txt">Updates</a>. (Mentions this sequence.)
%o (PARI) a(n) = { my (p = vector(n^2, k, (k-1)%n + ((k-1)\n)*I)); #setbinop((i,j)->[i+j, norm(i-j)], p)-n^2; } \\ _Rémy Sigrist_, Sep 24 2023
%Y Cf. A360351 (vertices), A360352 (regions), A360353 (edges), A360354 (k-gons), A359931.
%K nonn
%O 2,1
%A _Scott R. Shannon_, Feb 03 2023
%E More terms from _Rémy Sigrist_, Sep 24 2023
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