I've got an interesting question in combinatorics.
Given a number of constants $a$, $b$, $c$ and so on, where these constants are integers higher then one.
And there is also a constant $C$, which is also an integer higher then one. How many non-negative integer solutions are there for the equation: $$ax + by + cz + ... \leq C$$ Example: let's say we have 2 constants $a$ and $b$, with the respective values $5$ and $2$. Then there are $58$ different solutions for this equation given that $C = 30$. An example of a solution might be: $x = 0$ and $y = 0$ or $x = 5$ and $y = 2$. For this example I've graphed out all of the solutions in Geogebra with the red dots.
Could anyone maybe give some advice or give the solution to this problem. Any help would be greatly appreciated.