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A067151
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Number of regions in regular n-gon which are quadrilaterals (4-gons) when all its diagonals are drawn.
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12
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0, 0, 6, 7, 24, 36, 90, 132, 168, 234, 378, 600, 672, 901, 954, 1444, 1580, 2520, 2860, 2990, 3696, 4800, 5070, 6750, 7644, 9309, 7920, 12927, 12896, 15576, 16898, 20475, 18684, 25382, 27246, 30966, 32760, 37064, 37170, 45838, 47300, 55350, 60996, 69231, 66864, 80507, 87550, 98124, 103272
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OFFSET
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4,3
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REFERENCES
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B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.
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LINKS
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FORMULA
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Conjecture: a(n) ~ c * n^4. Is c = 1/64 ? - Bill McEachen, Mar 03 2024
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EXAMPLE
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a(6)=6 because the 6 regions around the center are quadrilaterals.
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CROSSREFS
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Cf. A007678, A067163, A064869, A067152, A067153, A067154, A067155, A067156, A067157, A067158, A067159.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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