Search: id:A092867
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%I A092867
%S A092867 12,75,252,715
%N A092867 Number of regions into which the line segments in A092866(n) cut a triangle.
%H A092867 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a092866.pdf">
               Intersections of diagonals in polygons of triangular shape.</a>
%H A092867 <a href="Sindx_Pol.html#Poonen">Sequences formed by drawing all diagonals 
               in regular polygon</a>
%e A092867 a(2)=12 because the 6 line segments mutually connecting the vertices 
               and the mid-side nodes form 12 congruent right triangles of two different 
               sizes.
%e A092867 a(3)=75: 48 triangles, 24 quadrilaterals and 3 pentagons are formed. 
               See pictures at Pfoertner link.
%Y A092867 Cf. A092866 Number of intersections, A092098 regions in triangle cut 
               by line segments connecting vertices with subdivision points on opposite 
               side, A006533 regions formed by all diagonals in regular n-gon, A002717 
               triangles in triangular matchstick arrangement.
%Y A092867 Sequence in context: A064121 A064116 A003368 this_sequence A053310 A006235 
               A009642
%Y A092867 Adjacent sequences: A092864 A092865 A092866 this_sequence A092868 A092869 
               A092870
%K A092867 more,nonn
%O A092867 2,1
%A A092867 Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 15 2004

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