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A137938 Number of 4-way intersections in the interior of a regular 6n-gon. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)."

LINKS

Table of n, a(n) for n=1..35.

Sequences formed by drawing all diagonals in regular polygon

EXAMPLE

a(3)=54 because there are 54 points in the interior of an 18-gon at which exactly four diagonals intersect.

CROSSREFS

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

Sequence in context: A124858 A183713 A126399 * A009726 A230920 A190948

Adjacent sequences:  A137935 A137936 A137937 * A137939 A137940 A137941

KEYWORD

nonn

AUTHOR

Graeme McRae, Feb 23 2008

STATUS

approved

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Last modified October 17 12:25 EDT 2019. Contains 328112 sequences. (Running on oeis4.)