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A187781
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Number of noncongruent polygonal regions in a regular n-gon with all diagonals drawn.
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3
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1, 1, 3, 3, 7, 7, 14, 14, 25, 21, 41, 40, 63, 60, 92, 72, 129, 121, 175, 166, 231, 192, 298, 285, 377, 360, 469, 350, 575, 553, 696, 666, 833, 744, 987, 956, 1159, 1123, 1350, 1165, 1561, 1508, 1793, 1741, 2047, 1875, 2324, 2255, 2625, 2563, 2951, 2761, 3303, 3214, 3682, 3588, 4089, 3695
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OFFSET
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3,3
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LINKS
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EXAMPLE
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a(5) = 3 since the 11 regions of a regular pentagon with all diagonals drawn consist of three different noncongruent polygons: two different triangles (each 5 times) and 1 pentagon.
a(6) = 3 since the 24 regions of the regular hexagon with all diagonals drawn consist of three different noncongruent polygons: 2 triangles (one 6 times, one 12 times) and 1 quadrilateral (6 times).
a(7) = 7 since the 50 regions of the regular heptagon with all diagonals drawn consist of seven different noncongruent polygons: 4 triangles (three 7 times, one 14 times), 1 quadrilateral (7 times), 1 pentagon (7 times) and 1 heptagon.
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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Corrected a(12) and a(16), extended from a(18) through a(60), corrected small typo in a(7) example - Christopher Scussel, Jun 23 2023
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STATUS
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approved
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