[seqfan] Re: Need help with puzzling sequence A118980
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
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 ...
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
>> 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
>> 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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