[seqfan] Re: Recurrence in A058865

[M. F. Hasler]

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.
>>
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>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>