[Python] Triangle of partition numbers in Python

I'm trying to make a dictionary corresponding to the triangle of partition numbers shown here:



So I want to replicate the (underlined red) recurrence relation and end up with:

{0: [1],
1: [1, 1],
2: [1, 1, 1],
3: [1, 2, 1, 1],
4: [1, 2, 2, 1, 1],
5: [1, 3, 3, 2, 1, 1]}


(I tried and failed to get the keys to equal n.) Here is my code:

dic1 = {}
for n in range(0,6):
dic1[n] = [1]
for i in range(0, 6):
if n > 0 and i > 0:
if i > n:
continue
elif n - i < i:
dic1[n].append(dic1[n-1][i-1])
else:
dic1[n].append(dic1[n-1][i-1] + dic1[n-i])
print(dic1)


Which gives:

{0: [1],
1: [1, 1],
2: [1, 2, 1],
3: [1, 3, 2, 1],
4: [1, 4, 4, 2, 1],
5: [1, 5, 6, 4, 2, 1]}


I just cannot see where I'm going wrong. Thank you.

Continue reading...