A372732 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 when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

7, 88, 438, 1567, 3910, 9504, 17905, 32833, 54066, 86365, 128380, 190152, 262699, 365761, 486711, 642154

Offset: 0

Author

Scott R. Shannon, May 12 2024

Keywords

• nonn
• more

Comments

A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.

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. A372731 (vertices), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372615, A371374, A353782, A360352.

Formula

a(n) = A372733(n) - A372731(n) + 1 by Euler's formula.