Catalan-like array with digits
Eric Angelini
Eric.Angelini at kntv.be
Tue Aug 21 12:02:09 CEST 2007
[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 ...
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