# [seqfan] Re: 1,6,110,2562,66222,...

Edwin Clark eclark at math.usf.edu
Mon Feb 9 17:20:23 CET 2009

```How are you getting the terms? If the sequence is given by T(2n,n) where T
is the array in
http://www.research.att.com/~njas/sequences/A103881
then using the formula there these are easy to compute.

Just to be clear the formula agrees with your values. So it is likely that
they are the same.

--Edwin

On Mon, 9 Feb 2009, rhhardin at att.net wrote:

> More terms
> 0 1
> 1 6
> 2 110
> 3 2562
> 4 66222
> 5 1815506
> 6 51697802
> 7 1511679210
> 8 45076309166
> 9 1364497268946
> 10 41800229045610
> 11 1292986222651646
> 12 40317756506959050
> 13 1265712901796074842
> 14 39965073938276694002
> 15 1268208750951634765562
> 16 40419340092267053380782
> 17 1293151592990764737265490
> 18 41512921146114663782643914
> 19 1336696804525969269347753334
> 20 43158316470769422985036007722
> 21 1396894744060840361583526359534
> 22 45313952186387344032141424880310
> 23 1472935673743661698205554658491142
> 24 47967219502930046234923103653158602
> 25 1564763324432611139054569034910940506
> 26 51125575601254146187206660714592557842
>
> --
> rhhardin at mindspring.com
> rhhardin at att.net (either)
>
> -------------- Original message ----------------------
> From: Edwin Clark <eclark at math.usf.edu>
>>
>>
>> Perhaps some one can extend this sequence:
>>
>> 1, 6, 110, 2562, 66222, ...
>>
>> The sequence arises in this paper mentioned today on the NMBRTHRY list:
>>
>> J.-M. Couveignes, T. Ezome and R. Lercier. Elliptic periods and
>> primality proving, (2008)
>> http://www.math.univ-toulouse.fr/~couveig/publi/arxiv3.pdf
>>
>> See section 8.6. The enumeration problem is:
>>
>> Find the number of integer sequences of length d = 2n+1 such that
>> the sum of the terms is 0 and the sum of the absolute values of the terms
>> is d-1.
>>
>> As the authors state the sum of the positive terms = sum of
>> absolute values of the negative terms = (d-1)/2.
>> So the largest interger in a desirable sequence is (d-1)/2.
>> I found the above terms for d = 1,3,5,7, 9  by brute force. Can someone do
>> better?
>>
>> The numbers appear in the array T(n,k) at
>> http://www.research.att.com/~njas/sequences/A103881
>> It looks like T(2n,n) works (if we define T(0,0)=1) but I don't see how to
>> prove it since I don't understand the definition of T(n,k).
>>
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>
>
>
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```