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A187781 Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn. 1
1, 1, 3, 3, 7, 7, 14, 14, 25, 22, 41, 40, 63, 61, 92 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Table of n, a(n) for n=3..17.

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 W. Weisstein, MathWorld: Regular Polygon Division by Diagonals

Index to sequences on drawing diagonals in regular polygons

EXAMPLE

a(5) = 3 since the 11 regions of the regular pentagon built by all diagonals consist of three different noncongruent polygons, i. e. 2 triangles (each 5 times) and 1 pentagon.

a(6) = 3 since the 24 regions of the regular hexagon built by all diagonals consist of three different noncongruent polygons, i. e. 2 triangles (one 6 times, one 12 times) and 1 quadrilateral (6 times).

a(7) = 7 since the 50 regions of the regular heptagon built by all diagonals consist of seven different noncongruent polygons, i. e. 4 triangles (three 7 times, one 14 times), 1 quadrilateral (7 times), 1 pentagon (7 times) and 1 heptagon.

CROSSREFS

Cf. A165217, A187782.

Sequence in context: A147449 A325344 A208474 * A263794 A086530 A147402

Adjacent sequences:  A187778 A187779 A187780 * A187782 A187783 A187784

KEYWORD

nonn,nice,more

AUTHOR

Martin Renner, Jan 05 2013

STATUS

approved

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Last modified May 27 05:24 EDT 2020. Contains 334649 sequences. (Running on oeis4.)