A372977 Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.

40, 553, 4204, 14505, 39004, 94365, 197464, 320925, 569600

Offset: 0

Author

Scott R. Shannon, May 19 2024

Keywords

• nonn
• more

Comments

A circle is constructed for every pair of the 4 + 4*n points, the first point defines the circle's center while the second the radius distance.

Links

• Scott R. Shannon, Image for n = 0. In this and other images the 4 + 4*n vertices forming the square are drawn larger for clarity.
• Scott R. Shannon, Image for n = 1.
• Scott R. Shannon, Image for n = 2.
• Scott R. Shannon, Image for n = 3.

Crossrefs

Cf. A372978 (regions), A372979 (edges), A372980 (k-gons), A372981 (circles), A372614, A372731, A371373, A354605, A360351.

Formula

a(n) = A372979(n) - A372978(n) + 1 by Euler's formula.