login
Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.
8

%I #9 May 12 2024 10:04:50

%S 6,51,301,1272,3285,8401,16050,30036,49801,80916,120447,180307,249108,

%T 350145,465898,618213

%N Number of vertices among all distinct circles that can be constructed from the 3 vertices and the equally spaced 3*n points placed on the sides of an equilateral triangle when every pair of the 3 + 3*n points are connected by a circle and where the points lie at the ends of the circle's diameter.

%C A circle is constructed for every pair of the 3 + 3*n points, the two points lying at the ends of a diameter of the circle.

%H Scott R. Shannon, <a href="/A372731/a372731.jpg">Image for n = 0</a>. In this and other images the 3 + 3*n vertices forming the triangle are drawn larger for clarity.

%H Scott R. Shannon, <a href="/A372731/a372731_1.jpg">Image for n = 1</a>.

%H Scott R. Shannon, <a href="/A372731/a372731_2.jpg">Image for n = 2</a>.

%H Scott R. Shannon, <a href="/A372731/a372731_3.jpg">Image for n = 3</a>.

%H Scott R. Shannon, <a href="/A372731/a372731_4.jpg">Image for n = 4</a>.

%F a(n) = A372733(n) - A372732(n) + 1 by Euler's formula.

%Y Cf. A372732 (regions), A372733 (edges), A372734 (k-gons), A372735 (number of circles), A372614, A371373, A354605, A360351.

%K nonn,more

%O 0,1

%A _Scott R. Shannon_, May 12 2024