cp's OEIS Frontend

A187781 Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn.

%I A187781 #44 Feb 16 2025 08:33:14
%S A187781 1,1,3,3,7,7,14,14,25,21,41,40,63,60,92,72,129,121,175,166,231,192,
%T A187781 298,285,377,360,469,350,575,553,696,666,833,744,987,956,1159,1123,
%U A187781 1350,1165,1561,1508,1793,1741,2047,1875,2324,2255,2625,2563,2951,2761,3303,3214,3682,3588,4089,3695
%N A187781 Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn.
%H A187781 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/drawing/drawing.html">Anzahl von Dreiecken eines regelmäßigen n-Ecks.</a>
%H A187781 Bjorn Poonen and Michael Rubinstein, <a href="http://math.mit.edu/~poonen/papers/ngon.pdf">The Number of Intersection Points Made by the Diagonals of a Regular Polygon</a>, SIAM J. Discrete Mathematics 11 (1998), nr. 1, pp. 135-156; doi: <a href="http://dx.doi.org/10.1137/S0895480195281246">10.1137/S0895480195281246</a>; arXiv: <a href="http://arXiv.org/abs/math.MG/9508209">math.MG/9508209</a>.
%H A187781 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygonDivisionbyDiagonals.html">Regular Polygon Division by Diagonals</a>.
%H A187781 <a href="/index/Pol#Poonen">Index to sequences on drawing diagonals in regular polygons</a>.
%e A187781 a(5) = 3 since the 11 regions of a regular pentagon with all diagonals drawn consist of three different noncongruent polygons: two different triangles (each 5 times) and 1 pentagon.
%e A187781 a(6) = 3 since the 24 regions of the regular hexagon with all diagonals drawn consist of three different noncongruent polygons: 2 triangles (one 6 times, one 12 times) and 1 quadrilateral (6 times).
%e A187781 a(7) = 7 since the 50 regions of the regular heptagon with all diagonals drawn consist of seven different noncongruent polygons: 4 triangles (three 7 times, one 14 times), 1 quadrilateral (7 times), 1 pentagon (7 times) and 1 heptagon.
%Y A187781 Cf. A006561, A007678, A165217, A187782.
%K A187781 nonn,nice
%O A187781 3,3
%A A187781 _Martin Renner_, Jan 05 2013
%E A187781 Corrected a(12) and a(16), extended from a(18) through a(60), corrected small typo in a(7) example - _Christopher Scussel_, Jun 23 2023