cp's OEIS Frontend

A358782 The number of regions 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 A358782 #28 Mar 25 2024 17:43:38
%S A358782 1,7,12,66,85,281,264,802,821,1893,1740,3810,3725,6871,6448,11748,
%T A358782 11125,18317,17160,27616,26797,40067,37176,56826,54653,77707,74788,
%U A358782 103734,101041,136835,131744,176584,172109,223931,216900,281090,273829,348583,337480,425950,416641
%N A358782 The number of regions 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 A358782 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 A358782 The author thanks Zach Shannon some of whose code was used in the generation of this sequence.
%C A358782 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 A358782 Scott R. Shannon, <a href="/A358782/a358782.jpg">Image for n = 2</a>. In this and other images the points defining the circle diameters are show as white dots.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_1.jpg">Image for n = 3</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_2.jpg">Image for n = 4</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_3.jpg">Image for n = 5</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_4.jpg">Image for n = 6</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_9.jpg">Image for n = 7</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_5.jpg">Image for n = 8</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_6.jpg">Image for n = 9</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_7.jpg">Image for n = 10</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_8.jpg">Image for n = 11</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_10.jpg">Image for n = 12</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_11.jpg">Image for n = 17</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_12.jpg">Image for n = 20</a>.
%H A358782 Scott R. Shannon, <a href="/A358782/a358782_13.jpg">Image for n = 23</a>.
%F A358782 a(n) = A358783(n) - A358746(n) + 1 by Euler's formula.
%Y A358782 Cf. A358746 (vertices), A358783 (edges), A359009 (k-gons), A007678, A344857.
%Y A358782 See allso A370976-A370979.
%K A358782 nonn
%O A358782 2,2
%A A358782 _Scott R. Shannon_, Nov 30 2022