cp's OEIS Frontend

A187782 Number of different kinds of polygons in a regular n-gon with all diagonals drawn.

%I A187782 #20 Feb 16 2025 08:33:14
%S A187782 1,1,2,2,4,2,5,3,5,2,6,3,6,4,7,5,7,5,6,6,7,4,7,6,7,6,9,4,8,5,7,6,8,6,
%T A187782 8,6,7,7,9,6,8,8,8,6,8,7,8,7,10,6,9,7,9,7,9,7,10,7
%N A187782 Number of different kinds of polygons in a regular n-gon with all diagonals drawn.
%H A187782 Sascha Kurz, <a href="http://www.mathe2.uni-bayreuth.de/sascha/oeis/drawing/drawing.html">Anzahl von Dreiecken eines regelmäßigen n-Ecks</a>.
%H A187782 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 A187782 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RegularPolygonDivisionbyDiagonals.html">Regular Polygon Division by Diagonals</a>.
%e A187782 a(5) = 2 since the 11 regions of the regular pentagon built by all diagonals consist of two different kinds of polygons, i.e., 10 triangles and 1 pentagon.
%e A187782 a(6) = 2 since the 24 regions of the regular hexagon built by all diagonals consist of two different kinds of polygons, i.e., 18 triangles and 6 quadrilaterals.
%e A187782 a(7) = 4 since the 50 regions of the regular heptagon built by all diagonals consist of four different kinds of polygons, i.e., 35 triangles, 7 quadrilaterals, 7 pentagons and 1 heptagon.
%Y A187782 Cf. A007678, A062361, A067151, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.
%K A187782 nonn,more
%O A187782 3,3
%A A187782 _Martin Renner_, Jan 05 2013
%E A187782 a(45)-a(60) from _Christopher Scussel_, Jun 24 2023