cp's OEIS Frontend

A341688 The number of regions inside 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 A341688 #16 Feb 20 2021 13:33:43
%S A341688 0,4,24,84,232,524,1052,1868,3144,4876,7440,10724,15124,20604,27632,
%T A341688 36124,46672,59108,74184,91488,112380,136044,163724,194924,230932,
%U A341688 271124,316992,367748,425124,488116,558820,635964,721824,815044,918132,1029524,1152012,1283788,1427964,1582328,1750760
%N A341688 The number of regions inside 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 A341688 The ellipse, with width twice its height, has points at its x-axis extrema and n-1 points both above and below the x-axis, 2n points in total. These are placed on the ellipse's perimeter by dividing it from the origin into 2n sectors of equal angle.
%C A341688 The terms are from numeric computation - no formula for a(n) is currently known.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688.png">Regions for n = 3</a>.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688_1.png">Regions for n = 5</a>.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688_2.png">Regions for n = 9</a>.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688_3.png">Regions for n = 19</a>.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688_4.png">Regions for n = 24</a>.
%H A341688 Scott R. Shannon, <a href="/A341688/a341688_5.png">Regions for n = 13 using random distance-based coloring</a>.
%H A341688 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ellipse">Ellipse</a>.
%Y A341688 Cf. A341762 (vertices), A341764 (edges), A341800 (n-gons), A007678, A092867, A255011, A331929, A331931, A333075.
%K A341688 nonn
%O A341688 1,2
%A A341688 _Scott R. Shannon_ and _N. J. A. Sloane_, Feb 17 2021