What Is the Recurrence Relation for the Sequence 1, 1, 2, 5, 12, 47?

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SUMMARY

The sequence 1, 1, 2, 5, 12, 47, 135... does not have a straightforward elementary recurrence relation, as indicated by forum participants. To derive a recurrence relation, one should analyze the differences between consecutive terms until a constant difference is achieved, which determines the polynomial degree of the relation. The discussion highlights that if a function f(n) is defined, such as f(n) = 2^n, it can still represent a recurrence relation, but it must be presented in the correct format for full credit. The sequence is not listed in Sloane's Encyclopedia of Integer Sequences, suggesting its complexity.

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Homework Statement


Find the recurrence relation to

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

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?
 
Last edited:
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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.
 
What happens if there is no elementary recurrence relation? What recurrence relation might it have then?
 
I can give you one more term in the recurrence relation,
1,1,2,5,12,47,135,...

It is most likely non elementary
 
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.
 
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?
 
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.
 
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?
 
No you should probably put it in the form I did for full marks.
 
  • #10
It's not in Sloane, surprisingly.
 
  • #11
maze said:
It's not in Sloane, surprisingly.

What do you mean? I don't understand.
 
  • #12
Sloane's rather comprehensive encyclopedia of integer sequences.
 

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