# Recurrence, for-loop and zero.

Hello guys! Hope you guys are having a nice day.

I have some problem as follows: I setup some recurrence as follows

```
def f(j,k):
if k==0:
m=j
elif j==0:
m=k
else:
m=j/k*(f(j-1,k)+1/k*(f(j-1,k)))+k/j*(f(j,k-1)+1/j*(f(j,k-1)))
return m
```

And if we calculate

```
f(1,1),
f(2,1),
f(1,2),
f(2,2)
```

in sage, then what we get are

4, 35/2, 35/2, 105/2.

However, if we do the for loop as in the below, I found the above results to be zero!!:

```
for k in range(3):
for j in range(3):
(j,k), expVal(j,k)
```

And the calculation result from the sage is:

((0, 0), 0)

((1, 0), 1)

((2, 0), 2)

((0, 1), 1)

**((1, 1), 0)**

**((2, 1), 0)**

((0, 2), 2)

**((1, 2), 0)**

**((2, 2), 0)**

And observe the bolded result above... it is weird that the result is zero... Can anyone help me fix this please...

Thank you for any help! Hope you have a nice rest of the day!