#OK to post homework 
#Zhizhang Deng, 09/27/2020, Assignment 6
1. 
because PIE is very slow in practice. Directly calculate the intersect/union is faster 
[seq(Pnx(n,x),n=1..7)] = [seq(PnxF(n,x),n=1..7)] 
PnxF is faster, Pnx takes longer. 
PnxF(30) is still 0.0 secs
Pnx(30) would take a long time because it need to do 2^30+2^29+... permutations

2. Because when k = 0, D(n) is kind of a specialization of PnxF where x = 0

3. 
i = 0 (A166)
i = 1 (A182390)
i = 2 (A387)
i = 3 (dont exist)

4. d(n) = (n-1)*(d(n-1) + d(n-2))