I am struggling with the following problem and I was hoping somebody could help me.
Solve by applying the convolution formula for generating functions: How many nonnegative integer solutions are there for $x_1 + 3x_2 = 100$?
I've been getting really high numbers in my attempts so far and there's no way that they are correct. If someone can help me get started that would be appreciated.
Thanks!
EDIT: Here is my work so far which is giving me the answer $176851$ solutions which I'm sure is wrong.
$G(x)=(1+x+x^2+x^3+...)(1+x^3+x^6+x^9+...)$ $G(x)=\left(\frac{1}{(1-x)}\right)\left(\frac{1}{(1-x^3)}\right)$
$a_n=1$ and
$b_n=\binom{n+2}{2}$
Then I'm finding the coefficient of $x^{100}$ from the convolution formula.