# [seqfan] Re: Delannoy numbers

Robert FERREOL robert.ferreol at gmail.com
Wed May 27 20:54:20 CEST 2020

```  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 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/
>>>
> --
> Seqfan Mailing list - http://list.seqfan.eu/

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