#0, difficult sequence, areas partitioned in circle ,
Posted by tommy on Dec-07-05 at 00:46 AM
THe question is the opposite of the famous one.
Take a circle, put on the inside of the circle (not on the circumference) any n points no three collinear. Make a chord between any two points. How many areas are partitioned by the chords.
For n=1 , you have one area, n=2 you have 2
for n=3 you have 7 areas. for n=4 you have 16
the sequence emerges
1,2,7, 16,31,54, ...
I dont see any pattern or recurrence.
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