Necklace Permutation Table
Enter a maximum n to list the necklace permutation count (n−1)!/2 for every size from n=3 up to n. Computed exactly with BigInt.
Input
Enter a maximum number n to list the necklace permutation count (n−1)!/2 from n=3 up to that size.
Enter a value from 3 to 50.
Result
Necklace permutations for n = 12
19,958,400
Necklace permutation table
The value of (n−1)!/2 for each n.
| Count n | Necklace count (n−1)!/2 |
|---|---|
| 3 | 1 |
| 4 | 3 |
| 5 | 12 |
| 6 | 60 |
| 7 | 360 |
| 8 | 2,520 |
| 9 | 20,160 |
| 10 | 181,440 |
| 11 | 1,814,400 |
| 12 | 19,958,400 |
Formula
Necklace count = (n−1)! ÷ 2
A necklace permutation treats reflections of a circular arrangement as the same, giving (n−1)!/2 for n of 3 or more.
How it works
- A necklace permutation counts the ways to arrange n distinct items in a circle where arrangements that match by rotation or by reflection (flipping) are treated as the same.
- The total is (n−1)!/2 arrangements, defined for n of 3 or more. For n of 3 or more, (n−1)! is always divisible by 2.
- This table lists the value of (n−1)!/2 for each row from n=3 up to the maximum n you enter.
- All values are computed exactly with BigInt so large counts stay precise.
- The maximum n can be set from 3 up to 50.
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Necklace Permutation Table