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A165217 Count of interior bounded regions in a regular 2n-sided polygon dissected by all diagonals parallel to sides. 3
6, 25, 50, 145, 224, 497, 630, 1281, 1606, 2761, 3302, 5265, 5940, 9185, 10472, 14977, 16834, 23161, 25284, 34321 (list; graph; refs; listen; history; text; internal format)



The rule is: get a regular polygon with at least 6 sides and an even number of sides (hexagon, octagon, etc.) and pick a point, then pick the point directly clockwise it, draw a line then draw lines parallel to it going through the other points. Then do the same with all the other points. a(n) is the count of interior bounded regions.

Please email me if you can find a pattern!


Table of n, a(n) for n=3..22.

R. J. Mathar, Tile Count in the Interior of Regular 2n-Gons Dissected by Diagonals Parallel to Sides, arxiv:0911.3434 [math.CO]

Index to sequences on drawing diagonals in regular polygons


Conjecture: a(2n) = (2*n-1)*(4*n^3-4*n^2+6*n-3)/3. - Thomas Young (tyoung(AT)district16.org), Dec 23 2018


Cf. A003454, A320422

Sequence in context: A079606 A184852 A067926 * A320422 A075224 A042185

Adjacent sequences:  A165214 A165215 A165216 * A165218 A165219 A165220




Chintan (timtamboy63(AT)gmail.com), Sep 08 2009


Values from a(6) to a(8) corrected, a(9) and a(10) added - R. J. Mathar, Oct 09 2009

Replaced URL by a more permanent arXiv link and added more terms - R. J. Mathar, Nov 19 2009

Typo in a(14) corrected. Thomas Young (tyoung(AT)district16.org), Dec 23 2018



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Last modified November 18 09:55 EST 2019. Contains 329261 sequences. (Running on oeis4.)