# Partial Recurrence Equation

Hey people

I have the following equation, which I don't manage to solve. The background of the problem is the clustergrowth of two chemical species, resulting in a final relation I'd like to solve:

$u_{n,m} = K_\alpha u_{n-1,m} A + K_\beta K_\gamma A B u_{n-1,m-1}$

with the conditions that

$u_{0,0} = S$

$u_{0,1} = 0$

$u_{1,0} = H_A \cdot A\cdot S$

$K_\alpha, K_\beta, K_\gamma, S$ are constants. $A$ increases $n$ by $1$, $B$ increases $m$ by $1$.

I appreciate your help. Cheers, riehen

-
The initial data you give are insufficient to determine the sequence uniquely from the given recursion. How are you going to find $u_{1,2}$, for instance? – fedja Dec 16 '11 at 18:19
Also, what do you mean by "A increases n by 1"? And what is $H_A$? – fedja Dec 16 '11 at 18:25