A350718 Number of regions in a regular n-gon with all diagonals drawn whose edges all have a different number of facing edges.
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
Offset: 3
Keywords
Examples
a(11) = 44. The 11-gon contains forty-four triangles whose three edges all have a different number of facing edges. This is the first n-gon to contain such regions. See the attached image.
Links
- Scott R. Shannon, Table of n, a(n) for n = 3..140
- Scott R. Shannon, Image for n = 11. This is the first n-gon 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 = 13.
- Scott R. Shannon, Image for n = 18.
- Scott R. Shannon, Image for n = 81. This is zoomed-in on one of the pentagons whose edges all have a different facing edge count: 6,7,8,9,10.
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