# Recurrent definiton of a function

Hi, I am trying to compose a code for calculating the numbers H01 defined as a sum of the following recursively defined numbers:

```
H11(r) = \sum_{a + b = r} a*b/r (H11(a) + H12(a)) * H11(b)
H12(r) = \sum_{a + b = r} a*b/r (H11(a) + H12(a)) * (H11(b) + H12(b))
H01(r) = H11(r) + H12(r)
```

I ended up with the following code:

```
memoH11 = {1:0, 2:1/2}
def H11(r1):
if memoH11.has_key(r1):
return memoH11[r1]
else:
a = 0
for j1 in range(1,r1):
a += j1*(r1 - j1)/r1 * (H11(j1) + H12(j1)) * H11(r1-j1)
memoH11[r1] = a
return a
memoH12 = {1:0, 2:0}
def H12(r2):
if memoH12.has_key(r2):
return memoH12[r2]
else:
b = 0
for j2 in range(1,r2):
b += j2*(r2 - j2)/r2 * ( H11(j2) + H12(j2) ) * ( H11(r2 - j2) + H12(r2-j2) )
memoH12[r2] = b
return b
def H01(r):
return H11(r) + H12(r)
```

And here problems start. If I just type

```
H01(8)
```

it produces the incorrect value 27/8. But if I type

```
H01(6), H01(8)
```

it results the correct tuple (7/6, 15/4).

So how to fix the code ? Thanks in advance for any help.

What are you trying to do!? You should explain it clearly and not only show your (wrong) functions. How should we guess!?

@vdelecroix, Thanks, I should have stated the problem more explicitly. I've added the setup to the question.

Great! Much better now ;-)