A372614 Number of vertices 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.

6, 87, 481, 1992, 6969, 15409, 35202, 58422, 107677, 159138, 268572, 350860, 557049

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.

Links

• Scott R. Shannon, Image for n = 0. In this and other images the 3 + 3*n vertices forming the triangle 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.
• Scott R. Shannon, Image for n = 4.

Crossrefs

Cf. A372615 (regions), A372616 (edges), A372617 (k-gons), A372682 (number of circles), A372731, A371373, A354605, A360351.

Formula

a(n) = A372616(n) - A372615(n) + 1 by Euler's formula.