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

Edwin Clark eclark at math.usf.edu
Sun Feb 8 22:53:35 CET 2009

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).