A371253 - OEIS

%I #19 Mar 25 2024 09:59:22

%S 1,1,6,5,26,18,99,89,270,271,650,516,1288,1303,2250,2337,4047,3636,

%T 6404,6401,9597,9769,14261,13632,20251,20125,27594,27749,37324,35040,

%U 49043,49185,63228,63547,80676,79380,101640,102259,125853,126561

%N 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.

%C See A371254 for further information.

%H Scott R. Shannon, <a href="/A371253/a371253.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_1.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_2.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_3.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_4.jpg">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_5.jpg">Image for n = 8</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_6.jpg">Image for n = 9</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_7.jpg">Image for n = 10</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_8.jpg">Image for n = 11</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_9.jpg">Image for n = 12</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_10.jpg">Image for n = 16</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_11.jpg">Image for n = 20</a>.

%H Scott R. Shannon, <a href="/A371253/a371253_12.jpg">Image for n = 24</a>.

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

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

%K nonn

%O 1,3

%A _Scott R. Shannon_, Mar 16 2024