so far i have seen all the recurrence relations(RR) similar to

F(n)= F(n-1)+F(n-2) .....the Fibonacci sequence

and they can be nonhomogeneous or of higher order.

but is there any method to solve equations like this

S(m,n)= S(m-1,n-1)+S(m,n-2)

i arrived at a RR similar to above when solving a 2 dimensional problem.

observe that S(m,n) need not be the same as S(n,m).