A373107 - OEIS

%I #7 May 26 2024 08:20:27

%S 12,136,932,3252,9144,20032,41260,71832,121460,188656,291488

%N Number of regions among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square when every pair of the 4 + 4*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

%C A circle is constructed for every pair of the 4 + 4*n points, the two points lying at the ends of a diameter of the circle.

%H Scott R. Shannon, <a href="/A373107/a373107.jpg">Image for n = 0</a>. In this and other images the 4 + 4*n vertices forming the square are drawn as white dots for clarity.

%H Scott R. Shannon, <a href="/A373107/a373107_1.jpg">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A373107/a373107_2.jpg">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A373107/a373107_3.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A373107/a373107_4.jpg">Image for n = 7</a>.

%F a(n) = A373108(n) - A373106(n) + 1 by Euler's formula.

%Y Cf. A373106 (vertices), A373108 (edges), A373109 (k-gons), A373110 (circles), A372978, A372732, A358782, A362234, A360352.

%K nonn,more

%O 0,1

%A _Scott R. Shannon_, May 25 2024