Homework Help: Find a recurrence relation

tgt · May 26, 2008

1. The problem statement, all variables and given/known data
Find the recurrence relation to

1,1,2,5,12,47,....

3. The attempt at a solution
Made all sorts of attempts. I'm not experienced with these things.

Was there a site that works these things out for you?

Gib Z · May 26, 2008

Do you have more terms? It might have no elementary relation. If you have more terms, list the difference between each consecutive terms. This forms a new sequence, do the same to this sequence. Keep doing it until the difference is a constant number. If it took you n times to do it, the relation is a polynomial of degree n.

tgt · May 26, 2008

What happens if there is no elementary recurrence relation? What recurrence relation might it have then?

tgt · May 26, 2008

I can give you one more term in the recurrence relation,
1,1,2,5,12,47,135,...

It is most likely non elementary

Defennder · May 26, 2008

Why don't you post the entire question here without truncating the series? Otherwise, it'll be difficult for the posters here to figure out the answer without even having the complete question to begin with.

tgt · May 27, 2008

Would it still be a recurrence relation if the relation was a function of n only? i.e a_n = f(n) where f(n) is a function of n.

What if a_n=f(n) where a_0 is in f(n)? Is a_n still a recurrence relation?

Gib Z · May 27, 2008

Depends what f(n) is. For example if f(n) = 2^n, then yours sequence is still the recurrence relation a_0 =1 , a_n+1 = 2 a_n.

tgt · May 27, 2008

Gib Z said: ↑

Depends what f(n) is. For example if f(n) = 2^n, then yours sequence is still the recurrence relation a_0 =1 , a_n+1 = 2 a_n.

So if the question stated give any recurrence relation and I wrote down f(n)=2^n and only that , would it be full marks?

Gib Z · May 27, 2008

No you should probably put it in the form I did for full marks.

maze · May 28, 2008

It's not in Sloane, surprisingly.

tgt · May 28, 2008

maze said: ↑

It's not in Sloane, surprisingly.

What do you mean? I don't understand.

maze · May 29, 2008

Sloane's rather comprehensive encyclopedia of integer sequences.

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