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A351129
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Number of regions in a regular n-gon with all diagonals drawn whose edges all have the same number of facing edges.
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2
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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
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OFFSET
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3,6
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COMMENTS
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See A351045 for details of an edge's count of facing edges in an n-gon with all diagonals drawn.
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LINKS
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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.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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