Find a generating function for the number of partitions of n satisfying all of the following: each part is 1,2,3, or 4, 1 appears as a part at most twice, 2 appears as a part an even number of times, and 3 appears as a part an odd number of times. Simplify your answer as much as possible. Then use this formula to find the number of such partitions of 20. A partition is counted by this sequence if and only if it has all of the 4 properties.