If I want to determine the number of positive integer solutions of , lets say, $$3a+4b+5c=91$$ this is equivalent to the number of non-negtaive integer solutions of $$3(a+1)+4(b+1)+5(c+1)=91$$ which can be written as $$3a+4b+5c=79$$
The coefficient of $x^{79}$ of the taylor-expansion of the generating function, in this case $$f(x)=\frac{1}{(1-x^3)(1-x^4)(1-x^5)}$$ is $60$ which is the solution.
A nice method, but can I calculate the number of non-negtative integer solutions with some formula containing multionomial-coefficients, stirling-numbers or similar terms ?