[seqfan] Re: Recurrence in A058865

Sean A. Irvine sairvin at gmail.com
Sat Sep 3 22:49:39 CEST 2022

Hi Maximilian,

Thank you for your effort on this one, and it looks to have been worthwhile
because it led to discovery of an error in the OEIS data for a(31).

Sean.

On Sun, 4 Sept 2022 at 04:59, M. F. Hasler <seqfan at hasler.fr> wrote:

> Update: I fixed the formula.
> The case  a(n, q=n*(n-1)/2) = 1
> has to be enforced explicitly.
> The PARI program now produces the table given in the paper and data in the
> sequence.
>
> - Maximilian
>
>
> On Sat, Sep 3, 2022 at 12:33 PM M. F. Hasler <seqfan at hasler.fr> wrote:
>
>> I think it's ok to keep offset 1, with an empty row 1 (row length
>> n(n-1)/2 = 0).
>> (Then the offset is the same for the columns.)
>>
>> I agree that the formula does not reproduce the values, for n < q <
>> n(n-1)/2,
>> thus, from row 4 on, for the values between the first nonzero element
>> a(n,n-1) = n
>> and the last elements a(n, n(n-1)/2) = 1.
>> I guess a combinatorial factor might be missing or be wrong, or
>> something's wrong with the indices.
>> (e.g., the second index k or q in a should be >= 1,
>>  but it is sometimes 0 in the recurrency : sum(L=0 .. q, ...).
>> (And what a bad idea to use a lowercase L  instead of \ell or some other
>> letter, like j !!))
>> Also suspicious : the 1/n within the sum (but doesn't depend on the
>> summation index).
>>
>> - Maximilian
>>
>>
>> On Fri, Sep 2, 2022 at 7:03 PM Sean A. Irvine <sairvin at gmail.com> wrote:
>>
>>> Hi,
>>>
>>> Can anyone get the recurrence in A058865 to work?
>>>
>>> I think the sequence offset should be 2, but even taking that into
>>> account
>>> and taking a(2,1)=1 as described in the Castelo and Wormald paper, I
>>> cannot
>>> get this recurrence to work.
>>>
>>> A program would be helpful.
>>>
>>> Sean.
>>>
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>