# [seqfan] Re: A family of quadratic recurrences

Charles Greathouse charles.greathouse at case.edu
Wed Sep 30 21:24:26 CEST 2009

```These double-exponential sequences are hard to work with!  I
calculated L < 5 and L > 9 to 35 terms and 5 <= L <= 9 to 30 terms to
verify that they are integers.  Some of the terms had hundreds of
millions of digits.  I suppose I could extend these with L additional
terms by working mod the last L terms.

On the slightly-related subject of other double exponentials (looked
up to compare to this sequence): A165421 is a duplicate of A011764
(differing only in offset).  Should this stay or be merged?  If
merged, should be recurrence be translated?
%F A011764 a(n) = 3 * a(1) * ... * a(n-1) for n > 1.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Sep 30, 2009 at 1:31 PM, Jaume Oliver i Lafont
<joliverlafont at gmail.com> wrote:
> Hello Seqfans,
>
> In the family of quadratic recurrences defined by
> a(n)=sum(i=1,L-1,a(n-i)*sum(j=i,L-1,a(n-j)))/a(n-L), with L initial ones,
> I have not been able to find any noninteger value.
>
> Do these recurrences yield only integers? For any L>=2?
>
> This search is related to sequence
> http://research.att.com/~njas/sequences/A165896,
> which is the case L=4.
>
> Regards,
> Jaume
>
>
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```