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Number of edges 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.
8

%I #36 Mar 20 2023 10:39:31

%S 212,2408,10548,28728,71588,149280,278716,461824

%N Number of edges 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 known.

%C See A354605 and A353782 for images of the vertices and regions.

%F a(n) = A353782(n) + A354605(n) - 1 by Euler's formula.

%Y Cf. A354605 (vertices), A353782 (regions), A361623 (k-gons), A361622 (distinct circles), A359934, A359861, A359254, A359571, A359047.

%K nonn,more

%O 1,1

%A _Scott R. Shannon_, Mar 13 2023