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

rhhardin at att.net rhhardin at att.net
Mon Feb 9 18:22:04 CET 2009

```It's brute force from the definition, not from EIS.

Albeit indirect brute force.

--
rhhardin at mindspring.com
rhhardin at att.net (either)

-------------- Original message ----------------------
From: Edwin Clark <eclark at math.usf.edu>
>
> 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/
> >
>
>
>
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```