[seqfan] Re: Linear recurrences with large gaps
Ron Hardin
rhhardin at att.net
Tue Jan 11 19:49:02 CET 2011
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?
(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)
----- Original Message ----
> From: Joerg Arndt <arndt at jjj.de>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Tue, January 11, 2011 1:28:45 PM
> Subject: [seqfan] Re: Linear recurrences with large gaps
>
> * Ron Hardin <rhhardin at att.net> [Jan 11. 2011 19:21]:
> > 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?
> >
>
> Hard to say:
>
> ? p=subst(p,a,x)+O(x^200)
> -1 + 2*x - x^2 + x^81 - 2*x^82 + x^83 + O(x^200)
> ? printprod(ser2prod(p)) \\ uses 'y' as symbol
> 1 * (1-y^1)^{2} * (1-y^81)^{1} \\ I should have noticed this earlier!
>
> That might be
> (1-y) * prod( n=1, oo, 1-y^(81^n) )
> which for oo == 2 is
> ? (1-y) * prod( n=0, 2, 1-y^(81^n) ) + O(y^9999)
> 1 - 2*y + y^2 - y^81 + 2*y^82 - y^83 - y^6561 + 2*y^6562 - y^6563 + y^6642 -
>2*y^6643 + y^6644 + O(y^9999)
>
> [but for now this is all just blind guessing]
>
> > rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
>
>
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