n划分为1，2，3等等（动态规划）

package bd_algo;

import java.util.Scanner;

public class coin {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int[] coins = {0, 1, 2, 3};
        while (in.hasNext()) {
            int n = in.nextInt();
            int[][] dp = new int[coins.length][n + 1];
            for (int i = 1; i < coins.length; i++) {
                for (int j = 0; j < n + 1; j++) {
                    if (j == 0) {
                        dp[i][j] = 1;
                        continue;
                    }
                    if(j - coins[i] >= 0) {
                        dp[i][j] = dp[i][j - coins[i]] + dp[i - 1][j];
                    }else {
                        dp[i][j] = dp[i -1 ][j];
                    }
                }
            }
            System.out.println(dp[3][n]);
        }
    }
}