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

R. J. Mathar, Tile Count in the Interior of Regular 2n-Gons Dissected by Diagonals Parallel to Sides, arxiv:0911.3434 [math.CO], 2009.

FORMULA

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

CROSSREFS

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

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

a(11)-a(22) from R. J. Mathar, Nov 19 2009

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

a(23)-a(43) from Christopher Scussel, Jun 25 2023

STATUS

approved