20 circles in the plane, all passing through the origin

Suppose I draw 20 circles in the plane, all passing through the origin, but no two tangent at the origin. Also, except for the origin, no three circles pass through a common point. How many regions are created in the plane?

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Answer

A hint:

Move the origin to using the map z1z. Then the circles become lines, no two of them parallel, and no three of them going through the same point.

Denote the number of regions created by n lines by an, and find a recursion for the an.

Attribution
Source : Link , Question Author : laser01 , Answer Author : Christian Blatter

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