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A137938
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Number of 4-way intersections in the interior of a regular 6n-gon.
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4
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0, 12, 54, 264, 420, 396, 1134, 1200, 1296, 3780, 2310, 2520, 3276, 3612, 4050, 5088, 5712, 5724, 7182, 11400, 9072, 9372, 10626, 11088, 12600, 13260, 14094, 15960, 17052, 23220, 19530, 20928, 21384, 23052, 26250
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OFFSET
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1,2
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COMMENTS
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When n is odd, there are no intersections in the interior of an n-gon where more than 2 diagonals meet.
When n is not a multiple of 6, there are no intersections in the interior of an n-gon where more than 3 diagonals meet except the center.
When n is not a multiple of 30, there are no intersections in the interior of an n-gon where more than 5 diagonals meet except the center.
I checked the following conjecture up to n=210: "An n-gon with n=30k has 5n points where 6 or 7 diagonals meet and no interior point other than the center where more than 7 diagonals meet; If k is odd, then 6 diagonals meet in each of 4n points and 7 diagonals meet in each of n points; If k is even, then no groups of exactly 6 diagonals meet in a point, while exactly 7 diagonals meet in each of 5n points (all points interior excluding the center)."
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LINKS
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EXAMPLE
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a(3)=54 because there are 54 points in the interior of an 18-gon at which exactly four diagonals intersect.
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CROSSREFS
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Cf. A000332: C(n, 4) = number of intersection points of diagonals of convex n-gon.
Cf. A006561: number of intersections of diagonals in the interior of regular n-gon.
Cf. A101363: number of 3-way intersections in the interior of a regular 2n-gon.
Cf. A101364: number of 4-way intersections in the interior of a regular n-gon.
Cf. A101365: number of 5-way intersections in the interior of a regular n-gon.
Cf. A137939: number of 5-way intersections in the interior of a regular 6n-gon
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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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