A359253 - OEIS

%I #17 Dec 24 2022 11:05:49

%S 3,14,51,116,255,466,821,1296,2003,2904,4171,5726,7795,10266,13399,

%T 17026,21537,26702,32995,40110,48511,57996,69121,81376,95511,111130,

%U 128953,148432,170595

%N Number of regions among all distinct circles that can be constructed from n equally spaced points along a line using only a compass.

%C A circle is constructed for every pair of the n points, the first point defines the circle's center while the second the radius distance. The number of distinct circles constructed for n points is A001859(n-1).

%C No formula for a(n) is currently known.

%H Scott R. Shannon, <a href="/A359253/a359253.jpg">Image for n = 2</a>. In this and other images the n points are shown as white dots.

%H Scott R. Shannon, <a href="/A359253/a359253_1.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_2.jpg">Image for n = 4</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_3.jpg">Image for n = 5</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_4.jpg">Image for n = 6</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_5.jpg">Image for n = 10</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_6.jpg">Image for n = 11</a>.

%H Scott R. Shannon, <a href="/A359253/a359253_7.jpg">Image for n = 20</a>.

%F a(n) = A359254(n) - A359252(n) + 1 by Euler's formula.

%Y Cf. A359252 (vertices), A359254 (edges), A359258 (k-gons), A001859, A290865, A359046, A358782.

%K nonn,more

%O 2,1

%A _Scott R. Shannon_, Dec 22 2022