cp's OEIS Frontend

A358746 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.

%I A358746 #33 Mar 25 2024 17:41:37
%S A358746 2,6,5,55,54,252,169,747,630,1804,1381,3679,3150,6690,5553,11509,9846,
%T A358746 18012,15241,27237,24398,39606,33577,56275,50622,77058,69693,102979,
%U A358746 94770,135966,124065,175593,162894,222810,205885,279831,260870,347178,321961,424391,399042
%N A358746 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 A358746 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 A358746 The author thanks Zach Shannon some of whose code was used in the generation of this sequence.
%C A358746 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 A358746 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 A358746 Scott R. Shannon, <a href="/A358746/a358746_6.jpg">Image for n = 3</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_7.jpg">Image for n = 4</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_8.jpg">Image for n = 5</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_9.jpg">Image for n = 6</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_10.jpg">Image for n = 7</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_11.jpg">Image for n = 8</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_12.jpg">Image for n = 9</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_13.jpg">Image for n = 10</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_14.jpg">Image for n = 16</a>.
%H A358746 Scott R. Shannon, <a href="/A358746/a358746_15.jpg">Image for n = 17</a>.
%F A358746 a(n) = A358783(n) - A358782(n) + 1 by Euler's formula.
%Y A358746 Cf. A358782 (regions), A358783 (edges), A359009 (k-gons), A007569, A146212.
%Y A358746 See allso A370976-A370979.
%K A358746 nonn
%O A358746 2,1
%A A358746 _Scott R. Shannon_, Nov 30 2022