# POJ 1286 Necklace of Beads （Polya）

## Description

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


## 思路

POJ 2409 Let it Bead （Polya） 的弱化版本，具体方法请戳左边链接。

## AC 代码

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<cmath>
#include<iostream>
using namespace std;
#include<queue>
#include<map>

int gcd(int a,int b)
{
if(b%a==0)return a;
return gcd(b%a,a);
}

int main()
{
int n;
while(cin>>n&&n!=-1)
{
if(n==0)
{
printf("0\n");
continue;
}
long long ans=0;
for(int i=1; i<=n; i++)
ans+=pow(3,gcd(i,n));
if(n&1)ans+=n*pow(3,n/2+1);
else ans+=n/2*(pow(3,n/2+1)+pow(3,n/2));
cout<<ans/n/2<<endl;
}
return 0;
}