# [seqfan] Re: Delannoy numbers

Neil Sloane njasloane at gmail.com
Tue May 26 06:29:27 CEST 2020

```"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
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 )

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 about
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/
>>
>
```