# Catalan-like array with digits

Eric Angelini Eric.Angelini at kntv.be
Tue Aug 21 12:02:09 CEST 2007

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[Marc] :
> Isn't the diagonal just the Catalan numbers under "casting out 9s" (...)

... indeed! Of course! My apologizes, and, as I said, "a stupid idea"!
Best,
É.

-----Message d'origine-----
De : Marc LeBrun [mailto:mlb at well.com]
Envoyé : lundi 20 août 2007 23:38
À : Eric Angelini; seqfan at ext.jussieu.fr
Objet : Re: Catalan-like array with digits

Isn't the diagonal just the Catalan numbers under
"casting out 9s" (ie mod 9, except 0-->9)?

At 02:05 PM 8/20/2007, Eric Angelini wrote:

>Hello SeqFan,
>a stupid idea :
>construct a Catalan-like generating array having only digits with the
>simple law: 1+1=2, 1+2=3, etc. 1+9=10=1+0=1, 5+5=10=1+0=1, 5+6=11=1+1=2,
>etc. and 9+9=18=1+8=9.
>The recursion is  N(x,y) = N(x-1,y) + N(x,y-1).              3  .  .  .  .
>                                                          6  3  9  6  3  9
>Is the diagonal chaotic?                               6  6  6  6  6  6  6
>Best,                                               6  6  9  9  9  9  9  9
>É.                                               9  6  9  3  9  9  9  9  9
>                                              9  9  6  3  3  6  9  9  9  9
>                                           9  9  9  6  6  9  3  3  9  9  9
>                                        4  9  9  9  6  9  3  3  9  6  9  9
>                                     4  4  5  9  9  6  3  3  9  6  6  3  9
>                                  7  4  9  1  4  9  6  6  9  6  6  9  6  6
>                               2  7  6  5  1  3  5  6  9  3  6  9  3  6  9
>                            2  2  5  8  8  5  2  2  1  3  3  3  3  3  3  3
>                         8  2  9  3  3  9  6  6  9  8  2  9  9  9  9  9  9
>                      6  8  3  7  3  9  6  6  9  3  8  3  7  9  9  9  9  9
>                   6  6  2  4  4  5  6  6  9  3  3  5  4  4  2  9  9  9  9
>                6  6  9  5  2  9  1  1  9  3  3  9  2  8  9  7  7  9  9  9
>             5  6  9  3  5  6  7  1  9  8  3  9  6  2  6  1  7  9  2  9  9
>          5  5  1  3  3  2  1  1  3  8  8  4  6  6  5  4  4  6  2  2  7  9
>       2  5  9  5  2  9  8  8  9  2  5  9  5  2  9  8  8  9  2  5  9  5  2
>    1  2  3  4  5  6  7  8  9  1  2  3  4  5  6  7  8  9  1  2  3  4  5  6
> 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 ...

```