A360352 - OEIS

%I #20 Sep 27 2023 14:58:16

%S 12,168,1536,8904,36880,123468,358036,912776,2105976

%N Number of regions 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="/A360352/a360352.jpg">Image for n = 2</a>. In this and other images the n X n grid points are shown as white dots.

%H Scott R. Shannon, <a href="/A360352/a360352_1.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A360352/a360352_2.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A360352/a360352_3.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A360352/a360352_4.jpg">Image for n = 6</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) - A360351(n) + 1 by Euler's formula.

%Y Cf. A360351 (vertices), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359933.

%K nonn,more

%O 2,1

%A _Scott R. Shannon_, Feb 04 2023