

A350718


Number of regions in a regular ngon with all diagonals drawn whose edges all have a different number of facing edges.


1



0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 130, 84, 180, 128, 374, 180, 418, 440, 714, 704, 1104, 624, 1750, 1976, 2484, 2744, 3190, 2880, 3658, 4416, 5280, 6188, 7000, 7128, 8214, 8892, 10296, 10560, 13120, 14028, 16082, 15928, 22140, 20332, 22466, 26112, 27538, 29200, 36924, 36504, 35934, 40284, 41140
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OFFSET

3,9


COMMENTS

See A351045 for details of an edge's count of facing edges in an ngon with all diagonals drawn.
For n = 3 to n = 80 the regions with edges all with a different number of facing edges are all triangles or quadrilaterals. The 81gon is the first ngon to contain pentagons with this property. The largest number of edges possible for such regions is unknown.


LINKS

Scott R. Shannon, Image for n = 11. This is the first ngon to contain regions whose edges all have a different facing edge count. In this and other images such regions are highlighted in gray.
Scott R. Shannon, Image for n = 81. This is zoomedin on one of the pentagons whose edges all have a different facing edge count: 6,7,8,9,10.


EXAMPLE

a(11) = 44. The 11gon contains fortyfour triangles whose three edges all have a different number of facing edges. This is the first ngon to contain such regions. See the attached image.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



