Search: id:A092866
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%I A092866
%S A092866 4,49,154,543
%N A092866 Number of intersections inside a triangular figure formed by the straight 
               line segments mutually connecting all vertices and all points that 
               divide the sides into n equal parts. If three or more lines meet 
               at an interior point this intersection is counted only once.
%C A092866 A detailed example for n=5 is given at the Pfoertner link.
%H A092866 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a092866.pdf">
               Intersections of diagonals in polygons of triangular shape.</a>
%H A092866 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>
%H A092866 <a href="Sindx_Pol.html#Poonen">Sequences formed by drawing all diagonals 
               in regular polygon</a>
%e A092866 a(2)=4 because there are 3 intersection points between the triangle medians 
               and the line segments connecting the midpoints of the sides plus 
               the intersection of the 3 medians at the centroid.
%Y A092866 Cf. A092867 regions formed by the diagonals, A006561 = number of intersections 
               of diagonals of regular n-gon, A091908 intersections between line 
               segments connecting vertices with subdivision points on opposite 
               side.
%Y A092866 Sequence in context: A147803 A112533 A016874 this_sequence A078187 A041065 
               A166838
%Y A092866 Adjacent sequences: A092863 A092864 A092865 this_sequence A092867 A092868 
               A092869
%K A092866 more,nonn
%O A092866 2,1
%A A092866 Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 10 2004

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