A362234 - OEIS

%I #7 Apr 14 2023 07:32:31

%S 32,372,1804,5772,14660,30816,58232,100080,161700,249200,368384

%N Number of regions among all distinct circles that can be constructed from a point on the origin and n equally spaced points on each of the +x,-x,+y,-y coordinates axes when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

%C A circle is constructed for every pair of the 1 + 4n points, the two points lying at the ends of a diameter of the circle. The number of distinct circles constructed from the points is A139275(n).

%C No formula for a(n) is currently known.

%H Scott R. Shannon, <a href="/A362234/a362234.jpg">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A362234/a362234_1.jpg">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A362234/a362234_2.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A362234/a362234_3.jpg">Image for n = 4</a>.

%F a(n) = A362235(n) - A362233(n) + 1 by Euler's formula.

%Y Cf. A362233 (vertices), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A353782, A359933.

%K nonn,more

%O 1,1

%A _Scott R. Shannon_, Apr 13 2023