HDU 1143 Tri Tiling （数学）

Tri Tiling

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 65536/32768K (Java/Other)

Total Submission(s) : 2   Accepted Submission(s) : 2

Problem Description

In how many ways can you tile a 3xn rectangle with 2x1 dominoes? Here is a sample tiling of a 3x12 rectangle.

 

Input

Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer 0 ≤ n ≤ 30.

 

Output

For each test case, output one integer number giving the number of possible tilings.

 

Sample Input

2 8 12 -1

 

Sample Output

3 153 2131

 如题 n>=4时有两种大方法来拼

第一种：

f(n)=f(n-2)*3;

第二种：

f(n)=2*f(n-4)+2*f(n-6)+......2*f(2)+2*f(0)

所以总f(n)= f(n-2)*3+2*f(n-4)+2*f(n-6)+......2*f(2)+2*f(0);

f(n)-f(n-2)=4*f(n-4)-f(n-2);

#include 
int main(int argc, char *argv[])
{
	long long a[31]={0};
	a[0]=1;
	a[2]=3;
	int i;
	for(i=4;i<31;i++)
	{
		if(i%2==1)
		continue;
		a[i]=a[i-2]*4-a[i-4];
	} 
	int n;
	while(scanf("%d",&n),n!=-1)
	{
		printf("%lld\n",a[n]);
	}
	return 0;
}