[seqfan] Re: A052996.

[Olivier Gerard]

On Fri, Dec 19, 2014 at 1:35 AM, L. Edson Jeffery <lejeffery2 at gmail.com>
wrote:
>
> Regarding https://oeis.org/A052996
>
> This sequence with its initial terms seems to be rather arbitrary. There
> are no references given, except for a link to the INRIA Encyclopedia of
> Combinatorial Structures which appears to be no longer available. So I
> wonder what the significance of A052996 is.
>
>
No, this sequence is not arbitrary. It has its place in a series of g.f. of
ascending
complexity. That was the purpose of the ECS, to enumerate basic g.f.s based
on their combinatorial definitions.

The formula given in the Maple line

spec := [S, {S=Prod(Union(Prod(Z, Z), Sequence(Z)), Sequence(Union(Z,
Z)))}, unlabeled ]:

corresponds to the specification of a combinatorial object
in the language of combstruct which is a publicly available Maple library
allowing to define such objects and compute things (terms, asymptotics,
...) about them.


> On the other hand, I have several new sequences and tables related to the
> Collatz 3x+1 problem which I have not submitted yet. One of them differs
> from A052996 only in its second entry. I would like to think that my
> sequence should stand on its own in the database as a new sequence (when I
> finally submit all of them), since it is a column of one of my arrays. What
> do the OEIS editors think about this?
>

This should be appreciated once you submit the relevant tables but we have
already entered sequences in the past differing by one or few initial
entries.
But please note that, as the o.g.f. of A052996 is simple, having deviation
in only one term means than your sequence should have a simple o.g.f. as
well.
It might be interesting for you to derive and prove it.


> Ed Jeffery
>
> p.s. Does anyone know what happened to ECS?
>
>
This project is now orphaned at INRIA for some time now.
We have already made inquiries about it. We will not suppress the links
right now but build a special index with more information and add
information about the combstruct system as well and refer to the
book by Flajolet and Sedgewick.