A372978 Number of regions 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.

45, 628, 4633, 15476, 41561, 98808, 206317, 333272, 590181

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 as white dots 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. A372977 (vertices), A372979 (edges), A372980 (k-gons), A372981 (circles), A372615, A371374, A353782, A360352.

Formula

a(n) = A372979(n) - A372977(n) + 1 by Euler's formula.