

A137939


Number of 5way intersections in the interior of a regular 6ngon.


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
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OFFSET

1,3


COMMENTS

When n is odd, there are no intersections in the interior of an ngon where more than 2 diagonals meet.
When n is not a multiple of 6, there are no intersections in the interior of an ngon 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 ngon where more than 5 diagonals meet except the center.
I checked the following conjecture up to n=210: "An ngon 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 18gon at which exactly five diagonals meet.


CROSSREFS

Cf. A000332: C(n, 4) = number of intersection points of diagonals of convex ngon..
Cf. A006561: number of intersections of diagonals in the interior of regular ngon.
Cf. A101363: number of 3way intersections in the interior of a regular 2ngon.
Cf. A101364: number of 4way intersections in the interior of a regular ngon.
Cf. A101365: number of 5way intersections in the interior of a regular ngon.
Cf. A137938: number of 4way intersections in the interior of a regular 6ngon.
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



