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**1. Homework Statement**

I am trying to find the number of nonnegative integer solutions to a+2b+4c=10^30. I found a generating function, and need to check the coefficient of 10^30.

**2. Homework Equations**

The generating function is 1/((1-x)(1-x^2)(1-x^4)). I found the PFD, which is -1/(8(x-1)^3) + 1/(4(x-1)^2) - 9/(32(x-1)) + 1/(16(1+x)^2) + 5/(32(1+x)) + (1+x)/(8(1+x^2))

**3. The Attempt at a Solution**

I need to simplify this into an equation using the Binomial Theorem. In class, we related each individual fraction to a series of some sort, or a combination and then combined them all into one equation, but I do not understand it at all. Please help!