cp's OEIS Frontend

A359046 Number of distinct regions among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass.

%I A359046 #22 Dec 15 2022 06:47:58
%S A359046 1,3,7,45,66,186,267,657,721,1501,1893,2772,3654,5727,6511,9969,11340,
%T A359046 14850,18051,23921,26755,35201,39975,47280,55776,69863,75385,93017,
%U A359046 102864,117810,134541,161217,172921,205293,221271,252828,277242,322811,341017,393721,420702,466074,509379
%N A359046 Number of distinct regions among all circles that can be constructed on vertices of an n-sided regular polygon, using only a compass.
%C A359046 See A331702 for further details.
%C A359046 No formula for a(n) is currently known.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046.jpg">Image for n = 2</a>. In this and other images the points defining the n-sided regular polygon are show as white dots.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_1.jpg">Image for n = 3</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_2.jpg">Image for n = 4</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_3.jpg">Image for n = 5</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_4.jpg">Image for n = 6</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_5.jpg">Image for n = 7</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_6.jpg">Image for n = 8</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_7.jpg">Image for n = 9</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_8.jpg">Image for n = 10</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_9.jpg">Image for n = 11</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_10.jpg">Image for n = 12</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_11.jpg">Image for n = 18</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_12.jpg">Image for n = 21</a>.
%H A359046 Scott R. Shannon, <a href="/A359046/a359046_13.jpg">Image for n = 25</a>.
%F A359046 a(n) = A359047(n) - A331702(n) + 1 by Euler's formula.
%Y A359046 Cf. A331702 (vertices), A359047 (edges), A359061 (k-gons), A358782, A007678.
%K A359046 nonn
%O A359046 1,2
%A A359046 _Scott R. Shannon_, Dec 14 2022