A374826 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 regions formed from all circle intersections.

1, 2, 6, 16, 80, 324, 1666, 3120, 17703, 28780, 115401, 96624, 528073, 589708

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.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 6.

Scott R. Shannon, Image for n = 8.

Scott R. Shannon, Image for n = 10.

Formula

a(n) = A374827(n) - A374825(n) + 1, by Euler's formula.

Crossrefs

Cf. A374825 (vertices), A374827 (edges), A374828 (k-gons), A007569 (total circles), A093005, A374337.

Sequence in context: A345246 A137858 A074740 * A204436 A135068 A147950

Adjacent sequences: A374823 A374824 A374825 * A374827 A374828 A374829

Keyword

nonn,more

Author

Scott R. Shannon, Jul 21 2024

Status

approved