# [seqfan] Re: Delannoy numbers

Neil Sloane njasloane at gmail.com
Sat May 30 21:37:15 CEST 2020

```Robert F. said:

(quote)
I always think that  D(n,k) , not D(n-k,k)  is the number of lattice
paths from (0,0) to (n,k) using steps (1,0), (0,1), (1,1).
(end)

Me:  I agree. I will correct the comment in A008288.

On Sat, May 30, 2020 at 12:25 AM Robert FERREOL <robert.ferreol at gmail.com>
wrote:

>   Hello,
>
>
> I allways think that  D(n,k) , not D(n-k,k)  is the number of lattice
> paths from (0,0) to (n,k) using steps (1,0), (0,1), (1,1).
>
> if  D(n,n) = http://oeis.org/A001850  is right, D(n,n)=A001850(n)=Number
> of paths from (0,0) to (n,n) in an n X n grid using only steps north,
> northeast and east (i.e., steps (1,0), (1,1), and (0,1)) ,  not D(n-n,n)
> ....
>
> Le 26/05/2020 à 06:29, Neil Sloane a écrit :
> > "mathcurves" said the other day that:
> >
> > 1) it should be said that T (n, k) = D (n-k, k) because it is not clear
> >
> > 2) D(n-k,k) is the number of lattice paths from (0,0) to (n,k) using
> >   - Joerg Arndt
> > <https://oeis.org/wiki/User:Joerg_Arndt>, Jul 01 2011
> > should be corrected into
> > D(n,k) is the number of lattice paths from (0,0) to (n,k) using steps
> > (1,0), (0,1), (1,1). (or D(i,j) because the entry says D(i,j) ?)
> >
> > 3) "Sum of n-th row = A000129 <https://oeis.org/A000129>(n). - Reinhard
> > Zumkeller <https://oeis.org/wiki/User:Reinhard_Zumkeller>, Dec 03 2004
> > "  and  "Row sums are A000129 <https://oeis.org/A000129>. - Roger L.
> > Bagula <https://oeis.org/wiki/User:Roger_L._Bagula>, Dec 09 2008 "   are
> > exactly the same and more precisely, it should be said :
> > Sum_{k=0..n} D(n-k,k) = Sum_{k=0..n} T(n,k) = A000129
> > <https://oeis.org/A000129>(n+1) (because A000129
> > <https://oeis.org/A000129>(0)=0 not 1 )
> >
> > Joerg,  could you take a look at this?  It seems to me that comment (1)
> > isn't needed, and perhaps indicates a slight confusion on the part of
> > "mathcurves" about the conventions that we use to convert arrays into
> > linear sequences (of course I may be wrong).  I have a similar worry
> > the second suggestion.  JJ, please take a look!
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Email: njasloane at gmail.com
> >
> >
> >
> > On Sat, May 23, 2020 at 10:59 PM Neil Sloane <njasloane at gmail.com>
> wrote:
> >
> >> Thanks for those updates to A008288 (I assume that is the sequence you
> are
> >> referring to).
> >> I will make the changes.
> >>
> >> Best regards
> >> Neil
> >>
> >> Neil J. A. Sloane, President, OEIS Foundation.
> >> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
> >> Email: njasloane at gmail.com
> >>
> >>
> >>
> >> On Wed, May 20, 2020 at 9:15 AM mathcurves <mathcurves at gmail.com>
> wrote:
> >>
> >>> Hello seqfans,
> >>>
> >>> I recently worked on the French page of delannoy numbers
> >>> https://fr.wikipedia.org/wiki/Nombre_de_Delannoy, and suggest
> >>> corrections on the corresponding page oeis
> >>>
> >>> 1) it should be said that T (n, k) = D (n-k, k) because it is not clear
> >>>
> >>> 2) D(n-k,k) is the number of lattice paths from (0,0) to (n,k) using
> >>> steps (1,0), (0,1), (1,1). - Joerg Arndt
> >>> <https://oeis.org/wiki/User:Joerg_Arndt>, Jul 01 2011
> >>> should be corrected into
> >>> D(n,k) is the number of lattice paths from (0,0) to (n,k) using steps
> >>> (1,0), (0,1), (1,1). (or D(i,j) because the entry says D(i,j) ?)
> >>>
> >>> 3) "Sum of n-th row = A000129 <https://oeis.org/A000129>(n). -
> Reinhard
> >>> Zumkeller <https://oeis.org/wiki/User:Reinhard_Zumkeller>, Dec 03 2004
> >>> "  and  "Row sums are A000129 <https://oeis.org/A000129>. - Roger L.
> >>> Bagula <https://oeis.org/wiki/User:Roger_L._Bagula>, Dec 09 2008 "
>  are
> >>> exactly the same and more precisely, it should be said :
> >>> Sum_{k=0..n} D(n-k,k) = Sum_{k=0..n} T(n,k) = A000129
> >>> <https://oeis.org/A000129>(n+1) (because A000129
> >>> <https://oeis.org/A000129>(0)=0 not 1 )
> >>>
> >>> Best regards
> >>>
> >>>
> >>> --
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
> --
>
> ROBERT FERRÉOL
> 6, Rue des Annelets 75019 PARIS
> 01 42 41 91 98
> http://mapage.noos.fr/r.ferreol