How many arrangements are there of n bits(0/1)on a circle if rotating one doesn't create different arrangement

This is known as the number of binary necklaces.

The numbers for n = 1,2,3,4,...,15 are:

2, 3, 4, 6, 8, 14, 20, 36, 60, 108, 188, 352, 632, 1182, 2192

For example, when n=5 we have:

00000

00001

00011

00101

00111

01011

01111

11111

And for n = 6,

000000

000001

000011

000101

001001

000111

001011

010011

010101

001111

010111

011011

011111

111111

This is not an easy problem to solve and is described here:

http://sue.csc.uvic.ca/~cos/inf/neck/NecklaceInfo....

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Each decision is basically a choice of 2. So for n = 3 choices its 2 x 2 x 2 i.e. 2^n

Since rotation is excluded and there are n different rotations representing the same thing

(2^n)/n