A362233 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 when each pair of points is connected by a circle and where the points lie at the ends of the circles' diameter.

17, 249, 1381, 4745, 12581, 26861, 51649, 89357, 145501, 225621, 335497

Offset: 1

Author

Scott R. Shannon, Apr 12 2023

Keywords

• nonn
• more

Comments

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).

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.
• Scott R. Shannon, Image for n = 4.

Crossrefs

Cf. A362234 (regions), A362235 (edges), A362236 (k-gons), A139275 (distinct circles), A354605, A359932.

Formula

a(n) = A362235(n) - A362234(n) + 1 by Euler's formula.