A371374 - OEIS

%I #16 Mar 22 2024 09:14:38

%S 1,1,9,9,51,48,211,217,612,651,1475,1248,3017,3193,5415,5793,9623,

%T 9000,15429,15901,23352,24311,34501,33840,49001,50337,67365,69385,

%U 91003,87720,120219,123169,155430,159291,198521,198792,250121,256121,310635,317441,382203,382032,465691,473573

%N Place n equally space points around the circumference of a circle and then, for each pair of points, draw two distinct circles, whose radii are the same as the first circle, such that both points lie on their circumferences. The sequence gives the total number of regions formed.

%C See A371373 and A371254 for further information. The details of the number of regions with k sides is given in A371376.

%H Scott R. Shannon, <a href="/A371374/a371374.jpg">Image for n = 3</a>. In this and other images the initial circle and n points are shown in white for clarity.

%H Scott R. Shannon, <a href="/A371374/a371374_1.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_2.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_3.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_4.jpg">Image for n = 7</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_5.jpg">Image for n = 8</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_6.jpg">Image for n = 9</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_7.jpg">Image for n = 10</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_8.jpg">Image for n = 11</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_9.jpg">Image for n = 12</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_10.jpg">Image for n = 15</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_11.jpg">Image for n = 20</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_12.jpg">Image for n = 24</a>.

%H Scott R. Shannon, <a href="/A371374/a371374_13.jpg">Image for n = 30</a>.

%F a(n) = A371375(n) - A371373(n) + 1 by Euler's formula.

%Y Cf. A371373 (vertices), A371375 (edges), A371376 (k-gons), A371377 (vertex crossings), A371254, A371253, A006533, A358782, A359046.

%K nonn

%O 1,3

%A _Scott R. Shannon_, Mar 20 2024