[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
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
More information about the SeqFan
mailing list