[seqfan] Re: Linear recurrences with large gaps
Joerg Arndt
arndt at jjj.de
Tue Jan 11 15:49:30 CET 2011
* 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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