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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.
5

%I #11 Jan 17 2021 11:23:11

%S 1,12,28,102,187,462,868,1590,3046,4398,6541,8646,12256,15336,20947,

%T 26610,33478,41832,50821,64710,77110,97878,113932,136560,160849,

%U 185220,216286,246450,289945,324594,372976,426936,472231,537366,598606,685650,762736,858546,943684,1043442,1143751,1258800

%N 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 The terms are from numeric computation - no formula for a(n) is currently known.

%H Scott R. Shannon, <a href="/A340685/a340685.png">Regions for n = 2</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_1.png">Regions for n = 3</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_2.png">Regions for n = 4</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_3.png">Regions for n = 6</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_4.png">Regions for n = 8</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_5.png">Regions for n = 10</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_6.png">Regions for n = 14</a>.

%H Scott R. Shannon, <a href="/A340685/a340685_7.png">Regions for n = 15</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circular_triangle">Circular triangle</a>.

%Y Cf. A340686 (vertices), A340687 (edges), A340688 (n-gons), A340639, A007678, A092867.

%K nonn

%O 1,2

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 16 2021