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A367015
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Number of regions formed after n points have been placed in general position on each edge of the triangle in A365929.
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8
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1, 4, 28, 136, 445, 1126, 2404, 4558, 7921, 12880, 19876, 29404, 42013, 58306, 78940, 104626, 136129, 174268, 219916, 274000, 337501, 411454, 496948, 595126, 707185, 834376, 978004, 1139428, 1320061, 1521370, 1744876, 1992154, 2264833, 2564596, 2893180, 3252376, 3644029, 4070038
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OFFSET
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0,2
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COMMENTS
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LINKS
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Scott R. Shannon, Image for n = 3. Note that although the number of k-gons will vary as the edge points change position the total number of regions will stay constant (at 136 for n = 3) as long as all internal vertices remain simple.
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FORMULA
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Conjecture: a(n) = (9*n^4 - 12*n^3 + 15*n^2 + 4)/4.
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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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