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

Fred Lunnon fred.lunnon at gmail.com
Tue Aug 13 00:21:30 CEST 2019

```  Apologies for attack of fat finger syndrome ...

What I intended to say was that I suspect the author made an elementary
error right at the top of the table: it should have commenced

1

2  1

5  5  2

...

Then the first column and final diagonals satisfy

T(n,0)  =  2 T(n-1,0) + T(n-2,0) ;

T(n,n-1)  =  n! (n+3)/2 ;

T(n,n)  =  n!  ;

Without more consistent data we're still snookered at this point ...

WFL

On 8/12/19, Fred Lunnon <fred.lunnon at gmail.com> wrote:
> 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
>> "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/
>>
>

```