Robert Munafo mrob27 at gmail.com
Wed Dec 2 02:04:12 CET 2009

```Michael Porter seems to be replying to my message about the recurrence
relation sequences webpage ( http://www.mrob.com/pub/math/MCS.html )
although he quotes my message about the Vincenzo Librandi sequences.

There is a specific and very important problem with linking OEIS entries to
any page on recurrence relations: Unless you can prove it, the recurrence
relation is just a conjecture.

In the case of the Vincenzo Librandi sequences, I can obviously prove the
formula because he gives the recurrence relation himself. But I was arguing
*against* the relevance of those sequences. I guess since we're probably
going to leave them in place, the link would make sense. But most of them
aren't mentioned on my webpage anyway, because I only list sequences with a
low "score" based on number of terms and magnitude of coefficients.

There is a more general case I discussed, which is that a large number of
OEIS sequences seem to have recurrence relations that are not currently
described in their individual OEIS entries. I use a broader definition of
"recurrence relation" that (for example) includes the factorials A000142.
There are probably hundreds of OEIS sequences I have found a formula for,
but even if all the terms match, *each would need to be proven* and that
takes a lot of work.

The OEIS index on recurrence relations,
http://research.att.com/~njas/sequences/Sindx_Rea.html#recLCC does not
mention the Vincenzo Librandi sequences, perhaps because it is the product
of manual effort, or some sort of periodic automatic process.

The most recent sequence in that index is A165192, authored in September. It
does not present its recurrence formula directly (which is
A[n+1]=A[n]-A[n-2]) but has a Python script which someone would have had to
read and translate. It does have a generating function, and there are enough
terms for computer analysis to reveal the formula.

Michael Porter wrote:
>
sequence.
>
> --- On Mon, 11/30/09, Robert Munafo wrote:
> [...]
> I don't think any of these sequences is too useful, but I also feel that
way about a lot of other things that are in OEIS. I'm a bit old-fashioned
and I still think existing publication should be a prerequisite (see
Handbook of Integer Sequences, section 1.5, rule 4) and that is why I create
a web page for each sequence before submitting it. But I recognize the fact
that I am outnumbered and a bit of an old relic in this regard.
>
> - Robert Munafo
>
> Alois Heinz wrote:
> > Paolo Lava schrieb:
> > > [...]
> > The sequence seems arbitrary and it is very simple, the given recursive
formula is too complicated.
> >
> > "a(n)=9*n-a(n-1)-6 (with a(1)=6)" is the same as
> >
> > "a(n)=9*floor((n+1)/2)-3" which is easier to understand and to evaluate.
> >
> > I can not imagine who would do a search on 6, 6, 15, 15, 24, 24, 33, 33,
42, 42, 51, 51, 60, 60, ...
> >
> > At least the keywords should be a combination of dumb,less,easy
> > [...]

--
Robert Munafo  --  mrob.com

```