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 A350718 Number of regions in a regular n-gon 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,9 COMMENTS See A351045 for details of an edge's count of facing edges in an n-gon 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 81-gon is the first n-gon to contain pentagons with this property. The largest number of edges possible for such regions is unknown. 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. EXAMPLE 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. CROSSREFS Cf. A351045, A351129, A135565, A007678, A342222, A349784. Sequence in context: A138086 A023933 A271141 * A022075 A178986 A174730 Adjacent sequences: A350715 A350716 A350717 * A350719 A350720 A350721 KEYWORD nonn AUTHOR Scott R. Shannon and N. J. A. Sloane, Feb 03 2022 STATUS approved

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Last modified August 5 01:22 EDT 2024. Contains 374934 sequences. (Running on oeis4.)