# Thread: Non Negative Integer Solutions...

1. ## Non Negative Integer Solutions...

I am expecting a similar problem on my upcoming exam. Any help would be greatly appreciated. Thanks a lot...

Let
hn denote the number of nonnegative integer solutions of the equation
2
e1 + 3e2 + 5e3 + 7e4 = n:

Find the generating function g(x) for h0, h1, h2,... hn....

2. If I want to find the number of non-negative integer solutions to 2e1 + 3e2 = 7, I will look for the coefficient of $x^7$ in

$(1 + x^2 + x^4 + ... )(1 + x^3 + x^6 + ... )$

Can you see why ?