[seqfan] Re: Linear recurrences with large gaps
Joerg Arndt
arndt at jjj.de
Wed Jan 12 09:41:12 CET 2011
* Ron Hardin <rhhardin at att.net> [Jan 12. 2011 09:26]:
> A much smaller gap of the same kind is
> http://oeis.org/A184258
> Empirical: a(n)=2*a(n-1)-a(n-2)+a(n-27)-2*a(n-28)+a(n-29)
> that also works out to 998; is that in range?
>
Yes:
? (1-a)^2*(1-a^27) /* recurrence as observed */
-a^29 + 2*a^28 - a^27 + a^2 - 2*a + 1
? (1-a)^2*(1-a^27)*(1-a^(27^2)) /* "next": */
a^758 - 2*a^757 + a^756 - a^731 + 2*a^730 - a^729 - a^29 + 2*a^28 - a^27 + a^2 - 2*a + 1
> (I could run things further but I'd have to transpose the code.
> It can do columns but not rows out beyond 1000.)
>
>
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
> [...]
Hints about how you compute (that many terms of) A184257
would be of interest for the computationalist btw.
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