[seqfan] Re: Linear recurrences with large gaps

[Joerg Arndt]

* 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]


> [...]