id:A092866 - OEIS Search Results

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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.

+0
2

4, 49, 154, 543 (list; graph; listen)

	OFFSET	`2,1`
	COMMENT	`A detailed example for n=5 is given at the Pfoertner link.`
	LINKS	`Hugo Pfoertner, Intersections of diagonals in polygons of triangular shape.` `Bjorn Poonen and Michael Rubinstein, The number of intersection points made by the diagonals of a regular polygon.` `Sequences formed by drawing all diagonals in regular polygon`
	EXAMPLE	`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.`
	CROSSREFS	`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.` `Sequence in context: A147803 A112533 A016874 this_sequence A078187 A041065 A166838` `Adjacent sequences: A092863 A092864 A092865 this_sequence A092867 A092868 A092869`
	KEYWORD	`more,nonn`
	AUTHOR	`Hugo Pfoertner (hugo(AT)pfoertner.org), Mar 10 2004`

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Last modified December 18 21:37 EST 2009. Contains 171024 sequences.

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