Find a recurrence relation from a sequence of integers

In summary, the conversation discusses finding the recurrence relation for a given sequence of integers using the formula An=xn+yn, where x and y are integers and n=0,1,2,3... There is also mention of solving recurrence relations and determining when they will have solutions of the form An = Bxn + Cyn.
  • #1
swtlilsoni
16
0
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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  • #2
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:
 

Related to Find a recurrence relation from a sequence of integers

1. How do I determine the recurrence relation for a sequence of integers?

To find a recurrence relation for a sequence of integers, you need to observe the pattern in the numbers. Look for any mathematical operations or relationships between the terms. You can also try to express the terms in terms of their previous terms or use a general formula to represent the sequence.

2. Can I use any sequence of integers to find a recurrence relation?

Yes, you can use any sequence of integers to find a recurrence relation. However, the sequence should follow a clear pattern or have a specific rule or relationship between the terms.

3. Is there a specific method or formula for finding a recurrence relation?

There is no one specific method or formula for finding a recurrence relation. However, there are some common techniques and strategies, such as identifying the pattern, using mathematical operations, or expressing terms in terms of their previous terms.

4. How can I verify if my recurrence relation is correct?

You can verify if your recurrence relation is correct by testing it on a few terms of the sequence. Plug in the terms into the recurrence relation and see if it produces the correct next term. You can also use induction or mathematical proof to verify the correctness of the recurrence relation.

5. Can a recurrence relation be used to generate an infinite sequence of integers?

Yes, a recurrence relation can be used to generate an infinite sequence of integers. As long as the relation is correct, it can be used to generate as many terms as needed in the sequence.

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