

A165217


Count of interior bounded regions in a regular 2nsided 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
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OFFSET

3,1


COMMENTS

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!


LINKS

Table of n, a(n) for n=3..22.
R. J. Mathar, Tile Count in the Interior of Regular 2nGons Dissected by Diagonals Parallel to Sides, arxiv:0911.3434 [math.CO]
Index to sequences on drawing diagonals in regular polygons


FORMULA

Conjecture: a(2n) = (2*n1)*(4*n^34*n^2+6*n3)/3.  Thomas Young (tyoung(AT)district16.org), Dec 23 2018


CROSSREFS

Cf. A003454, A320422
Sequence in context: A079606 A184852 A067926 * A320422 A075224 A042185
Adjacent sequences: A165214 A165215 A165216 * A165218 A165219 A165220


KEYWORD

nonn,more


AUTHOR

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


EXTENSIONS

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


STATUS

approved



