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A340639 The number of regions inside a Reuleaux triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.

%I A340639 #17 Jan 17 2021 11:30:08
%S A340639 1,24,145,516,1432,3084,6106,10638,17764,27336,41233,58902,82675,
%T A340639 111864,149497,194430,250534,316020,395728,487122,596434,720162,
%U A340639 865321,1027974,1216291,1425348,1664539,1928022,2226658,2553204,2920378,3319536,3764848,4246638,4780489,5355414,5988973
%N A340639 The number of regions inside a Reuleaux triangle formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.
%C A340639 The terms are from numeric computation - no formula for a(n) is currently known.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639.png">Regions for n = 2</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_1.png">Regions for n = 3</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_2.png">Regions for n = 4</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_3.png">Regions for n = 5</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_4.png">Regions for n = 6</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_5.png">Regions for n = 10</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_6.png">Regions for n = 11</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_7.png">Regions for n = 9 with random distance-based coloring</a>.
%H A340639 Scott R. Shannon, <a href="/A340639/a340639_9.png">Regions for n = 10 with random distance-based coloring</a>.
%H A340639 Wikipedia, <a href="https://en.wikipedia.org/wiki/Reuleaux_triangle">Reuleaux triangle</a>.
%Y A340639 Cf. A340644 (vertices), A340613 (edges), A340614 (n-gons), A007678, A092867.
%K A340639 nonn
%O A340639 1,2
%A A340639 _Scott R. Shannon_ and _N. J. A. Sloane_, Jan 14 2021