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A187782
Number of different kinds of polygons in a regular n-gon with all diagonals drawn.
2
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, 8, 6, 7, 7, 9, 6, 8, 8, 8, 6, 8, 7, 8, 7, 10, 6, 9, 7, 9, 7, 9, 7, 10, 7
OFFSET
3,3
LINKS
Bjorn Poonen and Michael Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics 11 (1998), nr. 1, pp. 135-156; doi: 10.1137/S0895480195281246, arXiv: math.MG/9508209.
Eric Weisstein's World of Mathematics, Regular Polygon Division by Diagonals.
EXAMPLE
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.
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.
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.
KEYWORD
nonn,more
AUTHOR
Martin Renner, Jan 05 2013
EXTENSIONS
a(45)-a(60) from Christopher Scussel, Jun 24 2023
STATUS
approved