A371253 Number of regions formed when n equally spaced points are placed around a circle and all pairs of points are joined by an interior arc whose radius equals the circle's radius.

1, 1, 6, 5, 26, 18, 99, 89, 270, 271, 650, 516, 1288, 1303, 2250, 2337, 4047, 3636, 6404, 6401, 9597, 9769, 14261, 13632, 20251, 20125, 27594, 27749, 37324, 35040, 49043, 49185, 63228, 63547, 80676, 79380, 101640, 102259, 125853, 126561

Offset: 1

Author

Scott R. Shannon, Mar 16 2024

Keywords

• nonn

Comments

See A371254 for further information.

Links

• 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 = 7.
• Scott R. Shannon, Image for n = 8.
• Scott R. Shannon, Image for n = 9.
• Scott R. Shannon, Image for n = 10.
• Scott R. Shannon, Image for n = 11.
• Scott R. Shannon, Image for n = 12.
• Scott R. Shannon, Image for n = 16.
• Scott R. Shannon, Image for n = 20.
• Scott R. Shannon, Image for n = 24.

Crossrefs

Cf. A371254 (vertices), A371255 (edges), A371274 (k-gons), A370980 (number of circles), A371374 (complete circles), A006533, A358782, A359046, A359253, A007678.

Formula

a(n) = A371255(n) - A371254(n) + 1 by Euler's formula.