[seqfan] Re: Recurrence in A058865

M. F. Hasler seqfan at hasler.fr
Sat Sep 3 18:33:00 CEST 2022

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 <
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/

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