cp's OEIS Frontend

A341762 The number of vertices on a 2 by 1 ellipse formed by the straight line segments mutually connecting all points formed by dividing the ellipse into 2n equal angle sectors from its origin.

%I A341762 #13 Feb 20 2021 13:34:11
%S A341762 2,5,19,65,195,461,971,1737,2995,4617,7203,10385,14779,20125,27155,
%T A341762 35481,46051,58277,73395,90323,111403,134765,162539,193385,229515,
%U A341762 269301,315331,365617,423195,485617,556603,633145,719299,811845,915275,1025921,1148811,1279757,1424395,1577723,1746803
%N A341762 The number of vertices on a 2 by 1 ellipse formed by the straight line segments mutually connecting all points formed by dividing the ellipse into 2n equal angle sectors from its origin.
%C A341762 See A341688 for a description of the ellipse.
%C A341762 Curiously the only ellipses found that have vertices with three or more lines crossing that are not on the x or y axes are those with a number of vertices equal to a multiple of ten.
%C A341762 The terms are from numeric computation - no formula for a(n) is currently known.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762.png">Image of the vertices for n = 3</a>.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762_1.png">Image of the vertices for n = 5</a>. Notice the off-axis vertices that have three lines crossing.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762_2.png">Image of the vertices for n = 9</a>.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762_3.png">Image of the vertices for n = 10</a>. Notice the off-axis vertices that have three or four lines crossing.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762_4.png">Image of the vertices for n = 20</a>. Notice the off-axis vertices that have three or more lines crossing.
%H A341762 Scott R. Shannon, <a href="/A341762/a341762_6.png">Image of the vertices for n = 21</a>.
%H A341762 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ellipse">Ellipse</a>.
%Y A341762 Cf. A341688 (regions), A341764 (edges), A341800 (n-gons), A007678, A092867, A255011, A331929, A331931, A333075.
%K A341762 nonn
%O A341762 1,1
%A A341762 _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 19 2021