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A137939 Number of 5-way intersections in the interior of a regular 6n-gon. 4
0, 0, 54, 24, 180, 216, 546, 336, 648, 720, 990, 936, 1404, 2352, 1890, 1824, 2448, 2592, 3078, 3720, 4284, 3960, 4554, 4464, 5400, 5616, 6318, 7896, 7308, 7560, 8370, 8256, 9504, 9792, 11550 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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 five diagonals meet.

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. A137938: number of 4-way intersections in the interior of a regular 6n-gon.

Sequence in context: A236178 A247389 A156476 * A033374 A247897 A247900

Adjacent sequences: A137936 A137937 A137938 * A137940 A137941 A137942

KEYWORD

nonn

AUTHOR

Graeme McRae, Feb 23 2008

STATUS

approved

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Last modified December 4 16:41 EST 2022. Contains 358563 sequences. (Running on oeis4.)