cp's OEIS Frontend

A360352 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.

%I A360352 #20 Sep 27 2023 14:58:16
%S A360352 12,168,1536,8904,36880,123468,358036,912776,2105976
%N A360352 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 A360352 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 A360352 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 A360352 Scott R. Shannon, <a href="/A360352/a360352_1.jpg">Image for n = 3</a>.
%H A360352 Scott R. Shannon, <a href="/A360352/a360352_2.jpg">Image for n = 4</a>.
%H A360352 Scott R. Shannon, <a href="/A360352/a360352_3.jpg">Image for n = 5</a>.
%H A360352 Scott R. Shannon, <a href="/A360352/a360352_4.jpg">Image for n = 6</a>.
%H A360352 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 A360352 a(n) = A360353(n) - A360351(n) + 1 by Euler's formula.
%Y A360352 Cf. A360351 (vertices), A360353 (edges), A360354 (k-gons), A360350 (distinct circles), A359933.
%K A360352 nonn,more
%O A360352 2,1
%A A360352 _Scott R. Shannon_, Feb 04 2023