A358746 - 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