Solve Recurrence Relation: A0,A1,A2 Given

swtlilsoni
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Homework Statement



An=3An-2-2An-3

When
A0=3
A1=1
A2=8

I tried to solve it normally like a normal recurrence relation however since it is not A sub n-1, it turns into a polynomial where the variable is raised to the third power which I couldn't factor and the whole thing turned into a mess.
 
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welcome to pf!

hi swtlilsoni! welcome to pf! :smile:

you mean x3 - 3x + 2?

can't you see one obvious root, just from looking at it? :wink:
 

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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