[seqfan] Re: Some number triangles
Olivier Gerard
olivier.gerard at gmail.com
Thu Apr 9 19:31:09 CEST 2015
On Thu, Apr 9, 2015 at 3:35 PM, Dale Gerdemann <dale.gerdemann at gmail.com>
wrote:
> Dear SeqFans,
>
>
> I've collected here some number triangles whose row sums are OEIS
> sequences. They all follow a basic parameterized formula. Most of these
> triangles are not in OEIS, and those that are in OEIS are usually defined
> with rather different formulae.
>
>
Dear Dale,
you have yourself noticed that the simplest cases are already in the OEIS,
for good reasons, as generalizations of the binomial and eulerian triangles.
Half of your triangles have simple and growing GCDs that should
probably be simplified, factored away, and the sums have simple
definitions. If you submit them as Neil suggested, please come
up with an idea of what they are counting (the binomial triangle
decomposes subsets by number of elements = binary words by number
of bits equal to 0 or 1, the eulerian triangle decomposes permutations
by, among other things, rises). It will give some motivations to these
entries.
You sent the link to your videos. Next time please do it for your
(proposed or not) sequences too instead of including them in a message.
It was much too big for the standards of that mailing list.
Regards,
Olivier
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