A374827 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 curved edges formed from all circle intersections.

1, 2, 9, 28, 150, 636, 3290, 6192, 35145, 57380, 230494, 192588, 1055535, 1177148

Offset

1,2

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.

Formula

a(n) = A374825(n) + A374826(n) - 1, by Euler's formula.

Crossrefs

Cf. A374825 (vertices), A374826 (regions), A374828 (k-gons), A007569 (total circles), A183207, A374339.

Sequence in context: A328281 A324372 A138912 * A002747 A110377 A338436

Adjacent sequences: A374824 A374825 A374826 * A374828 A374829 A374830

Keyword

nonn,more

Author

Scott R. Shannon, Jul 21 2024

Status

approved