[seqfan] Re: Need help with puzzling sequence A118980
fred.lunnon at gmail.com
Tue Aug 13 00:14:28 CEST 2019
T(n,n) = n! = n T(n-1,n-1) ;
T(n,n-1) = (n+1)T(n-1,n-2) - T(n-1,n-1) = n! (n+3)/2 ;
T(n,n-2) = ?
T(n,0) = 2 T(n-1,0) + T(n-2,0) ; fails for n = 2 ?!
T(n,1) = ?
On 8/12/19, Neil Sloane <njasloane at gmail.com> wrote:
> Dear SeqFans, I have been cleaning up some old sequences with keyword
> At the end of the weekend, this one is still a mystery: A118980. The
> puzzle boils down to this:
> What is the triangle?
> 2, 1;
> 6, 5, 2;
> 14, 22, 18, 6;
> 34, 85, 118, 84, 24;
> 82, 311, 660, 780, 480, 120;
> *All that is needed is a plausible guess for a way to continue this
> The left border is said to be the "companion Pell sequence A099425", and
> the right border is the factorials.
> There is an explicit definition in terms of a missing sequence referred to
> as "A118979" (different from the current A118979).
> There are more clues involving A118981, which also need editing, (Richard
> Mathar suggested a way to edit it in 2011, but I have not touched it
> because I did not want to disturb the crime scene).
> A118980 is a "cold case". Richard Mathar worked on it in 2011, and I
> struggled with it over the weekend. Now I'm calling in "The Wolf" - the
> combined minds of the Sequence Fans list. (The reference is to Pulp
> Seqfan Mailing list - http://list.seqfan.eu/
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