How do you solve third order recurrence relations?

swtlilsoni
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I know how to solve second order ones, but how would you solve third order ones? Because the characteristic polynomial would have a third degree so how can one find the roots?
I have looked everywhere online to find out but I can't find anything. Please Please tell me!
 
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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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