cp's OEIS Frontend

A340685 The number of regions inside a concave circular triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

%I A340685 #11 Jan 17 2021 11:23:11
%S A340685 1,12,28,102,187,462,868,1590,3046,4398,6541,8646,12256,15336,20947,
%T A340685 26610,33478,41832,50821,64710,77110,97878,113932,136560,160849,
%U A340685 185220,216286,246450,289945,324594,372976,426936,472231,537366,598606,685650,762736,858546,943684,1043442,1143751,1258800
%N A340685 The number of regions inside a concave circular triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
%C A340685 The terms are from numeric computation - no formula for a(n) is currently known.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685.png">Regions for n = 2</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_1.png">Regions for n = 3</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_2.png">Regions for n = 4</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_3.png">Regions for n = 6</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_4.png">Regions for n = 8</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_5.png">Regions for n = 10</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_6.png">Regions for n = 14</a>.
%H A340685 Scott R. Shannon, <a href="/A340685/a340685_7.png">Regions for n = 15</a>.
%H A340685 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circular_triangle">Circular triangle</a>.
%Y A340685 Cf. A340686 (vertices), A340687 (edges), A340688 (n-gons), A340639, A007678, A092867.
%K A340685 nonn
%O A340685 1,2
%A A340685 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 16 2021