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Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < 24 ). If the repetitions that are produced by rotation around the center of the circular necklace or reflection to the axis of symmetry are all neglected, how many different forms of the necklace are there?

Input The input has several lines, and each line contains the input data n.
-1 denotes the end of the input file.
Output The output should contain the output data: Number of different forms, in each line correspondent to the input data. Sample Input

4
5
-1

Sample Output

21
39

模板題， 當然是直接上板子啦；
有對Polya定理不懂的小夥伴點這裏 ： 傳送門

#include<iostream>
#include<cmath>

using namespace std;
#define ll long long

ll Pow(int value,int num)
{   __int64 sum=1;
    for(int i=1;i<=num;i++)
        sum*=value;
    return sum;
}

int gcd(int a, int
 
 b)
{
    if(b) return gcd(b, a%b);
    else return a;
}

ll polya(int col, int num)  // col 表示顏色種類， num 表示換環的長度
{
    ll sum = 0;
    for(int i = 1; i <= num; i++)
    {
        sum += Pow(col, gcd(num,i));
    }
    if(num&1) sum += num*(Pow(col, num/2+1));
    else sum += (Pow(col, num/2) + Pow(col, num/2+1))*(num/2);
    return sum/2/num;

}

int main()
{
    int n;
    while(cin >> n, n != -1)
    {
        if(n == 0) cout << 0 << endl;
        else
        {
            ll ans = polya(3,n);
            cout << ans << endl;
        }

    }
    return 0;
}

Necklace of Beads （polya定理的引用）