A354605 Number of vertices 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.

101, 1145, 5001, 13753, 34497, 72185, 135157, 224321

Offset: 1

Author

Scott R. Shannon, Mar 13 2023

Keywords

• nonn
• more

Comments

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).

No formula for a(n) is currently known.

Links

• Scott R. Shannon, Image for n = 1.
• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.

Crossrefs

Cf. A353782 (regions), A356358 (edges), A361623 (k-gons), A361622 (distinct circles), A359932, A359859, A359252, A359569, A331702.

Formula

a(n) = A356358 - A353782(n) + 1 by Euler's formula.