[seqfan] Re: Sequences with simple recurrence definitions

[Robert Munafo]

It is good to be discussing this before we get the wiki fully operational,
as it will surely come up a lot as people start adding sequences "on their
own".

What Franklin writes, is generally what I am thinking -- there should
be *multiple
independent criteria *for "intersting-ness". I think the old "academic
publication" rule was a manifestation of this. Publication implies that the
sequence is interesting both to the author and to an intended audience.

The "rule of 2" sounds like a really good way to express it. For example,
being generated by a smple formula is interesting, and having an application
in some field is another type of interesting. Both would be needed to submit
the sequence. That would be enough to exclude all the countless recurrence
relation sequences.

Franklin T. Adams-Watters wrote:
> I tend to use a "rule of 2" for new sequences.  If I can find 2 apparently
unrelated facts about a sequence, even if individually those facts are not
very interesting, I will usually submit it.
>
> Of course, even one fact that falls (IMO) into the "definitely
interesting" category is enough to get me to submit the sequence.
>
> I would say that the criteria for what sequences -- once submitted --
should be accepted are more lax than this.  Still, I think people should be
discouraged from submitting large numbers of similar sequences about each of
which only one independent, not very interesting fact is known.
>
> Any staggered sequence of two (or more) linear sequences will have a
fairly simple formula and several recurrence relations, including a linear
recurrence, and hence a rational generating function.  Thus, something else
would be required for such a sequence in order to meet the rule of 2
criterion.

--
Robert Munafo  --  mrob.com