dp

• f[n]是投n次骰子得到的点数序列，有
• $f[n] = (a_{n}, a_{n+1},\dots, a_{6 * n})$；
• $f[n-1] = (b_{n - 1}, b_{n},\dots, b_{6 * (n - 1)})$
• 得到a_{n} = b_{n - 1}(n=1)，a_{n + 1} = b_{n-1}(n=2) + b_{n}(n=1)....其中（n=1）代表投第n次时骰子数值为1，因此投第n次的点数是上一次前最多6个数的和。

class Solution(object):
    def numberOfDice(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        init = [1, 1, 1, 1, 1, 1]
        for _ in range(2, n + 1):
            res, window, count = [], [], 0
            for num in init:
                if window and len(window) == 6:
                        count -= window.pop(0)
                window.append(num)
                count += num
                res.append(count)
            while window:
                count -= window.pop(0)
                if count:
                    res.append(count)
            init = res
        return init