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

[rhhardin at att.net]

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

--
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).
> 
> 
> 
> 
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