Solve 8c Stamp Problem with Recurrence Relation

Punkyc7
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Use a recurrence relation to find the number of ways that stamps that have a value of 1 cent , 2 cents and a 3 cents can add up to eight cents.

How exactly do you go about solving a problem like this without writing a program to find all the possibilities?

The answer given is 81, but I have know Idea how to get it.
 
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How would you interpret the coefficient of x^8 in the expansion of (x+x^2+x^3)^n?

RGV
 
Would that be the number of times a certain combination happens?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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