I'm trying to solve (find a closed-form solution to) this (Risk odds calculator) recurrence relation:

```
p[n,m] == 2890/7776*p[n,m-2] + 2611/7776*p[n-1,m-1] + 2275/7776*p[n-2,m],
p[n,1] == 855/1296 + 441/1296*p[n-1,1],
p[3,m] == 295/1296*p[3,m-2] + 420/1296*p[2,m-1],
p[2,m] == 55/216,
p[1,m] == 0
```

Mathematica's RSolve function doesn't work (I'm sure I'm using the right syntax, since I'm following the two-variable examples at http://reference.wolfram.com/mathematica/ref/RSolve.html).

In fact, RSolve won't even solve this "simpler" recursion:

```
p[n,m] == p[n,m-2] + p[n-1,m-1] + p[n-2,m],
p[0,m] == 1,
p[1,m] == 1,
p[n,1] == 1,
p[n,0] == 1
```

Is there something fundamentally hard about solving this type of recurrence relation or is Mathematica just being flaky?

The exact example I'm using:

```
RSolve[{
p[n,m] == p[n,m-2] + p[n-1,m-1] + p[n-2,m],
p[0,m] == 1,
p[1,m] == 1,
p[n,1] == 1,
p[n,0] == 1
}, p[n,m], {n,m}]
```

The return value is the same as my input, up to some number juggling.

On the doc page, it's under "Scope" and then "Partial Difference Equations"

## comments: