# [seqfan] Re: Linear recurrences with large gaps

Ron Hardin rhhardin at att.net
Tue Jan 11 19:16:34 CET 2011

Running the series for the three recurrences out to n=998 shows that the
existing recurrences work, at least out that far.

Is that far enough to exclude the further term guess?

rhhardin at mindspring.com
rhhardin at att.net (either)

----- Original Message ----
> From: Joerg Arndt <arndt at jjj.de>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Tue, January 11, 2011 9:49:30 AM
> Subject: [seqfan] Re: Linear recurrences with large gaps
>
> * Ron Hardin <rhhardin at att.net> [Jan 11. 2011  15:42]:
> > That looks like a likely guess!  (owing to an array limit  in bc(1) I can't
>do
>
> > recurrences over a(n-99))
> > [...]
>
> Just  email the sequence, I'll then use
> http://www.jjj.de/pari/ser2prod.gpi
>
>
> > [...]
> >
> >  Empirical: a(n)=2*a(n-1)-a(n-2)+a(n-81)-2*a(n-82)+a(n-83)
> >
>
> ?  p=-1+2*a^1-a^2+a^81-2*a^82+a^83
> a^83 - 2*a^82 + a^81 - a^2 + 2*a - 1
> ?  factor(p)
> [a - 1 3]
> [a^2 + a + 1 1]
> [a^6 + a^3 + 1 1]
> [a^18 + a^9 +  1 1]
> [a^54 + a^27 + 1 1]
>
>
> >  [...]
>
>
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