Find a recurrence relation from a sequence of integers

[swtlilsoni]

If you are given a sequence of integers such as:
A_n=xⁿ+yⁿ
where x and y are integers. and n=0,1,2,3...
how would one find the recurrence relation?

I tried writing A_n+1 in terms of A_n 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?

 

[tiny-tim]

hi swtlilsoni!

i assume you know how to solve recurrence relations such as A_n+2 + pA_n+1 + qA_n = 0 ?

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