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

1,3

Links

Table of n, a(n) for n=1..14.

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.

Formula

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

Crossrefs

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

Sequence in context: A042277 A125617 A197969 * A121452 A249165 A304598

Adjacent sequences: A374816 A374817 A374818 * A374826 A374827 A374828

Keyword

nonn,more

Author

Scott R. Shannon, Jul 21 2024

Status

approved