A374825 Place n equally spaced points on the circumference of a circle of radius r and then connect each pair of points with straight lines whose intersections create A007569(n) - n additional points. Draw a circle of radius r around each of the A007569(n) points. The sequence gives the total number of vertices formed from all circle intersections.

0, 1, 4, 13, 71, 313, 1625, 3073, 17443, 28601, 115094, 95965, 527463, 587441

Offset: 1

Author

Scott R. Shannon, Jul 21 2024

Keywords

• nonn
• more

Links

• Scott R. Shannon, Image for n = 2. In this and other images the starting circles' centers are shown as white dots.
• Scott R. Shannon, Image for n = 3.
• Scott R. Shannon, Image for n = 4.
• Scott R. Shannon, Image for n = 5.
• Scott R. Shannon, Image for n = 6.
• Scott R. Shannon, Image for n = 9.

Crossrefs

Cf. A374826 (regions), A374827 (edges), A374828 (k-gons), A007569 (total circles), A370980, A374338.

Formula

a(n) = A374827(n) - A374826(n) + 1, by Euler's formula.