[seqfan] Re: integer sequence that is the sum of two or more known integer sequences

[Brad Klee]

Hi David,

I like your sequence, the graph is complicated and interesting compared to
some similar sequences I have looked at recently.

Can you compute Generating Functions for your sequences? Or is there a
reason to expect no simple Generating Functions to exist?

In simple examples with diophantine constraints, I used the generating
functions to find a lot of linear relations. You may want to take a look at:

http://list.seqfan.eu/pipermail/seqfan/2015-July/015083.html

I think there is an argument against including _any_ linear relations. Some
have meanings we understand, but are other linear relations meaningless or
just incomprehensible to us?

Unless there is special meaning or practical use to the linear relations, I
don't believe in listing them. In my personal opinion, It's taking the OEIS
in the wrong direction and introducing lots of clutter. You have already
found one or two linear relations, but how many more exist in the OEIS? I
would wager there are some linear relations you hvae yet to find.

What should we do instead of listing linear relations?

I think it is a good idea to define a set of spanning sequences for some
vector space, then ennumerate the belongings of that vector space. Or
possibly consider a ring of formal power series generated by some
expansions. Which sequences have expansions belonging to this ring?

I think that the vector space / ring question is of fundamental importance
to understanding connections in the OEIS. Has anyone investigated this
angle yet?


Thanks,

Brad




On Fri, Jul 31, 2015 at 9:27 AM, David Corneth <davidacorneth at gmail.com>
wrote:

> I've just put up two sequences, A260803 and A260804, which are the
> difference of two sequences. Now, A071693 <https://oeis.org/A071693> and
> A071689 <https://oeis.org/A071689> will be the sum of two ('known'?)
> sequences as well.
>
> Best,
> David
>
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