burnside

论文：http://baxterweb.com/puzzles/burnside5.pdf

n种颜色，染魔方，方案数为ans%1e9。

ans=(n^6+3*k^4+12*k^3+8*k^4)/24;

 1 #include<cstdio>
 2 #define ll long long
 3 const ll mod=1e9+7;
 4 ll pow_(ll a,ll b,ll mod)
 5 {
 6     ll ans=1,temp=a%mod;
 7     while(b)
 8     {
 9         if(b&1) ans=ans*temp%mod;
10         b>>=1;
11         temp=temp*temp%mod;
12     }
13     return ans%mod;
14 }
15 ll inv(ll a,ll mod)
16 {
17     return pow_(a,mod-2,mod);
18 }
19 ll ans;
20 int main()
21 {
22     int t;
23     ll n;
24     scanf("%d",&t);
25     while(t--)
26     {
27         ans=0;
28         scanf("%lld",&n);
29         ans=(ans+pow_(n,6,mod))%mod;
30         ans=(ans+pow_(n,4,mod)*3%mod)%mod;
31         ans=(ans+pow_(n,3,mod)*12%mod)%mod;
32         ans=(ans+pow_(n,2,mod)*8%mod)%mod;
33         printf("%lld
",ans*inv(24,mod)%mod);
34     }
35 }