[seqfan] Re: Mathematica code for A050446.

Alonso Del Arte alonso.delarte at gmail.com
Wed Dec 14 20:28:24 CET 2011

Yes, it does correctly generate the table in A050446. I tried in
Mathematica 7.0, but it should work in all earlier versions, too.

Actually, I am once again impressed by Mathematica's intelligence: I
thought I was going to have to remove the ">"s from the program after I
pasted it into Mathematica, but Mathematica realized this and automatically
removed the extraneous ">"s.


On Wed, Dec 14, 2011 at 6:29 AM, Richard Mathar
<mathar at strw.leidenuniv.nl>wrote:

> http://list.seqfan.eu/pipermail/seqfan/2011-December/016078.html
> > From seqfan-bounces at list.seqfan.eu Wed Dec 14 11:14:52 2011
> > Date: Tue, 13 Dec 2011 21:42:55 -0800 (PST)
> > From: Ed Jeffery
> > To: "seqfan at list.seqfan.eu" <seqfan at list.seqfan.eu>
> > Subject: [seqfan] Mathematica code for A050446.
> >
> > Could someone please verify the Mathematica code for A050446 (
> https://oeis.org/A050446) and let me know if it correctly generates the
> table given in the example there? I can't get the right table using Mathcad
> even single-stepping through the calculations according to that code. The
> Mathematica code is:
> >
> > t[n_, m_?Positive] := t[n, m] = t[n, m-1] + Sum[t[2k, m-1]*t[n-1 -
> > 2k, m], {k, 0, (n-1)/2}]; t[n_, 0] = 1; Table[t[i-k , k-1], {i, 1, 12},
> > {k, 1, i}] // Flatten
> >
> > I think the second part of the code, Table[t[etc.]], which I can't do in
> Mathcad, just reads the array t[n,m] by anti-diagonals transforming the
> array into a table, although I have no experience with Mathematica. I also
> assumed that the implied range for k in the summation is {k, 0,
> floor((n-1)/2)}, since in the summation using Mathcad I have to have
> (n-1)/2 a positive integer. Maybe someone could take a minute to give me a
> detailed description of what that code actually does, since evidently I
> have misunderstood it somehow.
> >
> The Mma code seems to be a rewriting of the formula. The formula is
> correct and can be also worked out in Maple (which I did): start the column
> m=0 with all-1, and use recursively a summation over k=0 up to
> floor((n-1)/2).
> The bad thing of the Mma code is that it uses a second index summation
> starting at 1, where 0 would be the natural choice because rows and columns
> are indexed from 0 upwards.
> In the maple code I use the variable "d" (for diagonal, 0 increasing) and
> then a
> column index m=0 up to d, and a row index n=d-m.
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Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

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