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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Table of n, a(n) for n=3..44.

Sascha Kurz, Anzahl von Dreiecken eines regelmäßigen n-Ecks.

Bjorn Poonen, 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, Regular Polygon Division by Diagonals (MathWorld).

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.

CROSSREFS

Cf. A007678, A062361, A067151, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.

Sequence in context: A057567 A217895 A005128 * A129296 A300837 A321443

Adjacent sequences:  A187779 A187780 A187781 * A187783 A187784 A187785

KEYWORD

nonn,more

AUTHOR

Martin Renner, Jan 05 2013

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)