[seqfan] Re: LRS formulas for n>=...?

Richard Mathar mathar at strw.leidenuniv.nl
Sun Aug 2 16:51:27 CEST 2009

Continuing http://list.seqfan.eu/pipermail/seqfan/2009-August/002013.html

rh> From: rhhardin at att.net
rh> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
rh> Date: Sun, 02 Aug 2009 13:13:23 +0000
rh> Subject: [seqfan] Re: LRS formulas for n>=...?
rh> It makes more sense to have that automated, then, doesn't it?  The coefs can
rh> be thought of as implicit in the given series, if they're there, at least for
rh> empirically generated ones like mine that just turn up or don't; and some
rh> series crawler will put them in the right index.

This was what placed many of the Plouffe "conjectures" into the database,
but it turned out that one must anyway return to the actual definition of
the sequence to ensure that the recurrences are not just intermediate behavior
of something more complicated...referring to the discussion in the May 2008 incarnation
of the seqfan group.

As the database is supposed to contain the verified truth, it's a scaring
option to automate the detection. One could in some way collect
all the apparent recurrences by running some sort of superseeker across the
entire database and put them in some index, but that would remain labeled
by "use with caution".

rh> Does the cited page require the entire series obey the formula from the first term?
rh> (I'm getting what must be a boundary condition effect for a few terms, before the
rh> formulas kick in.)

What currently is in the index allows some transient terms with
deferred validity of the recurrence. The explicit entry in the
main database then reveals when the recurrence starts. So all of your
examples would have made it into one line of the index, although there are
one or two low indices where the recurrences do not apply.

Note that this is just a deliberate choice that I made collecting the
entries, because for recurrences--like for series--these initial terms are
often not very interesting or set arbitrarily by the authors. I am willing
to change this kind of filtering if there is a majority vote in favor.

Richard Mathar


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