How many signs?

How many different signs are there? Or, to make the question slightly more definite, how many signs can you make with 1 circle, 2 circles, 3 circles, and so on? In general, how many signs can you make with n circles?

Here are the answers up to n=4 circles (not forgetting n=0):

n	Signs consisting of n circles	Number of signs
0		1
1		1
2		2
3		4
4		9

You may like to work out a few more for yourself. In case you do, the results for n=5,6,... etc are not given here, but are to be found on the next page.

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