Find a recurrence relation from a sequence of integers

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To find a recurrence relation from the sequence An = xn + yn, one must express An+1 in terms of An, but this can be complex due to the mixed powers of n. The challenge arises when trying to simplify the expression, as it does not translate neatly. Understanding how to solve standard recurrence relations, such as An+2 + pAn+1 + qAn = 0, is crucial for this process. The discussion hints at exploring solutions of the form An = Bxn + Cyn to potentially simplify the problem. Ultimately, identifying a clear recurrence relation requires careful manipulation of the terms involved.
swtlilsoni
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If you are given a sequence of integers such as:
An=xn+yn
where x and y are integers. and n=0,1,2,3...
how would one find the recurrence relation?

I tried writing An+1 in terms of An but it doesn't come out neatly because it doesn't translate so well. And there are terms raised to the n+1 multiplied by terms raised to the n. Am I going about it the wrong way?
 
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hi swtlilsoni! :smile:

i assume you know how to solve recurrence relations such as An+2 + pAn+1 + qAn = 0 ?

ok, then when will it have solutions of the form An = Bxn + Cyn ? :wink:
 

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