[seqfan] Re: Need help with puzzling sequence A118980

[John W. Nicholson]

Maybe there is a hint here: A118980
John W. Nicholson 

    On Sunday, August 11, 2019, 10:00:19 PM CDT, Neil Sloane <njasloane at gmail.com> wrote:  
 
 PS Probably someone will see the answer right away.  If not,
and if I had an assistant, I would say:
Siri, there are fewer than 20K sequences with keyword tabl.
so make a list of all those that are lower triangular matrices with top
left entry 1.
Take all the 6X6 upper triangular matrices with top left entry 1.
Call this list L.
We are trying to find the matrix A,

[1, 0, 0, 0, 0, 0;

2, 1, 0, 0, 0, 0;

6, 5, 2, 0, 0, 0;

14, 22, 18, 6, 0, 0;

34, 85, 118, 84, 24, 0;

82, 311, 660, 780, 480, 120]



Siri, please take every entry B in the list L,
and see if any of B*A, inverse(B)*A, A*B, A*inverse(B) are in L.
If so, tell me, and I will set you free.




On Sun, Aug 11, 2019 at 10:03 PM Neil Sloane <njasloane at gmail.com> wrote:

>
> Dear SeqFans, I have been cleaning up some old sequences with keyword
> "uned".
> At the end of the weekend, this one is still a mystery: A118980.  The
> puzzle boils down to this:
> What is the triangle?
>
> 1;
>
> 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
> triangle.*
>
>
> 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
> Fiction.)
>
>
>

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