A372615 Number of regions among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle, using only a compass.

7, 121, 624, 2368, 7912, 17115, 38461, 63184, 115614, 170149, 285715, 371982, 588043

Offset: 0

Author

Scott R. Shannon, May 07 2024

Keywords

• nonn
• more

Comments

A circle is constructed for every pair of the 3 + 3*n points, the first point defines the circle's center while the second the radius distance.

The vertices of the initial equilateral triangle are indicated by small circles in the illustrations here.

Links

• Scott R. Shannon, Image for n = 0.
• 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. A372614 (vertices), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A371374, A353782, A360352.

Formula

a(n) = A372616(n) - A372614(n) + 1 by Euler's formula.