Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #33 Mar 25 2024 17:41:37
%S 2,6,5,55,54,252,169,747,630,1804,1381,3679,3150,6690,5553,11509,9846,
%T 18012,15241,27237,24398,39606,33577,56275,50622,77058,69693,102979,
%U 94770,135966,124065,175593,162894,222810,205885,279831,260870,347178,321961,424391,399042
%N The number of vertices formed when every pair of n points, placed at the vertices of a regular n-gon, are connected by a circle and where the points lie at the ends of the circle's diameter.
%C Conjecture: for odd values of n all vertices are simple, other than those defining the diameters of the circles. No formula for n, or only the odd values of n, is currently known.
%C The author thanks Zach Shannon some of whose code was used in the generation of this sequence.
%C If n is odd, the circle containing the initial n points is not part of the graph (compare A370976-A370979). - _N. J. A. Sloane_, Mar 25 2024
%H Scott R. Shannon, <a href="/A358746/a358746_5.jpg">Image for n = 2</a>. In this and other images the points defining the circle diameters are show as white dots.
%H Scott R. Shannon, <a href="/A358746/a358746_6.jpg">Image for n = 3</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_7.jpg">Image for n = 4</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_8.jpg">Image for n = 5</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_9.jpg">Image for n = 6</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_10.jpg">Image for n = 7</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_11.jpg">Image for n = 8</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_12.jpg">Image for n = 9</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_13.jpg">Image for n = 10</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_14.jpg">Image for n = 16</a>.
%H Scott R. Shannon, <a href="/A358746/a358746_15.jpg">Image for n = 17</a>.
%F a(n) = A358783(n) - A358782(n) + 1 by Euler's formula.
%Y Cf. A358782 (regions), A358783 (edges), A359009 (k-gons), A007569, A146212.
%Y See allso A370976-A370979.
%K nonn
%O 2,1
%A _Scott R. Shannon_, Nov 30 2022