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%I #17 Sep 27 2023 14:57:57
%S 5,77,1045,6885,30265,104421,309973,800185,1862053
%N Number of vertices among all 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. The number of distinct circles constructed from the n X n grid is A360350(n).
%H Scott R. Shannon, <a href="/A360351/a360351.jpg">Image for n = 2</a>.
%H Scott R. Shannon, <a href="/A360351/a360351_1.jpg">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A360351/a360351_2.jpg">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A360351/a360351_3.jpg">Image for n = 5</a>.
%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.)
%F a(n) = A360353(n) - A360352(n) + 1 by Euler's formula.
%Y Cf. A360352 (regions), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359932.
%K nonn,more
%O 2,1
%A _Scott R. Shannon_, Feb 03 2023
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