A353782 - OEIS

%I #35 Mar 20 2023 10:39:40

%S 112,1264,5548,14976,37092,77096,143560,237504

%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 using only a compass.

%C A circle is constructed for every pair of the 1 + 4n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed from the points is A361622(n).

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

%H Scott R. Shannon, <a href="/A353782/a353782.jpg">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A353782/a353782_1.jpg">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A353782/a353782_2.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A353782/a353782_3.jpg">Image for n = 4</a>.

%F a(n) = A356358 - A354605(n) + 1 by Euler's formula.

%Y Cf. A354605 (vertices), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359933, A359860, A359253, A359570, A359046.

%K nonn,more

%O 1,1

%A _Scott R. Shannon_, Mar 13 2023