HDU1396 Counting Triangles

Problem Description
Given an equilateral triangle with n the length of its side, program to count how many triangles in it.




 

Input
The length n (n <= 500) of the equilateral triangle's side, one per line.

process to the end of the file
 

Output
The number of triangles in the equilateral triangle, one per line.
 

Sample Input
1
2
3
 

Sample Output
1
5
13

#include<stdio.h>
#include<string.h>
int main(){
    long long a[505];
    a[1]=1;
    for(int i=2;i<505;i++){
        a[i]=a[i-1]+(2*i-1)+(i*(i-1))/2;
        int k=i-3;
        while(k>0){
            a[i]=a[i]+k;
            k=k-2;
        }
    }
    int n;
    while(scanf("%d",&n)!=EOF){
        printf("%lld\n",a[n]);
    }
    return 0;
}

思路：

        边长为n的三角形的个数=边长为（n-1）的三角形的个数+第n层新增的边长为1三角形的个数+边长大于1的三角形的个数+倒三角形的个数

        a[n]=a[n-1]+(2*n-1)+(n*(n-1))/2+(n-3)+(n-5)+直到n为0停止

        a[1]=1,a[2]=5,a[3]=13,a[4]=27,a[5]=48,

        a[4]=13+7+6+1

        a[5]=27+9+10+2

        a[6]=48+11+15+3+1