# [seqfan] Re: Need help with puzzling sequence A118980

Georg.Fischer georg.fischer at t-online.de
Mon Aug 12 11:13:32 CEST 2019

```Dear Neil,

the difference of the two last terms in each row
gives n!/2 (~ A001710)

I think Richard was on the right track. I suppose
that the current A118979 has nothing to do with that
suite of sequences of Gary W. Adamson, and that Gary
had submitted a different A118979 which is lost, respectively
which was reconstructed as the array K(n,k) in the comment
in A118980 by Richard.

Best regards - Georg

Am 12.08.2019 um 05:00 schrieb Neil Sloane:
> 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.)
>>
>>
>>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>

--
Dr. Georg Fischer, Rotteckring 19, D-79341 Kenzingen
Tel. (07644) 913016, +49 175 160 7788, www.punctum.com

```