A372977 - OEIS

%I #8 May 19 2024 08:53:50

%S 40,553,4204,14505,39004,94365,197464,320925,569600

%N Number of vertices among all distinct circles that can be constructed from the 4 vertices and the equally spaced 4*n points placed on the sides of a square, using only a compass.

%C A circle is constructed for every pair of the 4 + 4*n points, the first point defines the circle's center while the second the radius distance.

%H Scott R. Shannon, <a href="/A372977/a372977.jpg">Image for n = 0</a>. In this and other images the 4 + 4*n vertices forming the square are drawn larger for clarity.

%H Scott R. Shannon, <a href="/A372977/a372977_1.jpg">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A372977/a372977_2.jpg">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A372977/a372977_3.jpg">Image for n = 3</a>.

%F a(n) = A372979(n) - A372978(n) + 1 by Euler's formula.

%Y Cf. A372978 (regions), A372979 (edges), A372980 (k-gons), A372981 (circles), A372614, A372731, A371373, A354605, A360351.

%K nonn,more

%O 0,1

%A _Scott R. Shannon_, May 19 2024