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A351129
Number of regions in a regular n-gon with all diagonals drawn whose edges all have the same number of facing edges.
2
1, 0, 1, 0, 1, 8, 1, 0, 1, 132, 66, 56, 46, 144, 171, 576, 305, 620, 652, 616, 852, 1296, 1376, 1482, 1891, 1820, 2379, 4530, 3163, 3328, 3532, 4046, 4656, 4896, 6661, 6460, 7411, 7560, 9595, 11676, 10923, 13552, 10936, 13294, 14806, 17232, 17935, 17200, 20452, 20540, 24964, 27270
OFFSET
3,6
COMMENTS
See A351045 for details of an edge's count of facing edges in an n-gon with all diagonals drawn.
LINKS
Scott R. Shannon, Image for n = 5. In this and other images the regions with edges with the same facing edge count are highlighted in the corresponding edge color.
Scott R. Shannon, Image for n = 8.
Scott R. Shannon, Image for n = 12.
Scott R. Shannon, Image for n = 15.
Scott R. Shannon, Image for n = 18.
Scott R. Shannon, Image for n = 24.
EXAMPLE
a(5) = 1. A pentagon with all diagonals drawn contains a central pentagon which is surrounded by five other triangles and therefore all its edges have a facing edge count of 6. See the attached image.
a(8) = 8. An octagon with all diagonals drawn contains eight central triangles all of which are surrounded by three other triangles and therefore all their edges have a facing edge count of 4. See the attached image.
a(15) = 46. A 15-gon with all diagonals drawn contains one central 15-gon which is surrounded by triangles, thirty quadrilaterals which are surrounded by other quadrilaterals, and fifteen triangles which are surrounded by pentagons. This gives a total of forty-six regions whose edges all have the same facing edge count. See the attached image.
KEYWORD
nonn
AUTHOR
STATUS
approved