class Solution(object):
    def combinationSum4(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
nums = [1, 2, 3]
target = 4

f(4) = [1,f(3)] if 1 in nums U [2, f(2)] if 2 in nums U [3, f(1)] if 3 in nums U [4, f(0)] if 4 in nums

The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)        
        """
        dp = [1] + [0]*target
        for x in range(1, target+1):
            for n in nums:
                if x >= n:
                    dp[x] += dp[x-n]
        return dp[target]