[math-fun] better posed problem? (small progress)

[David Wilson]

NJAS:

The following mail conjectures that A103314(30) = 146854.  I can definitely 
tell
you that as it stands in database, A103314(30) = 1336336 is incorrect, and 
the
sequence should be truncated back to A103314(29) until A103314(30) is
confirmed.

----- Original Message ----- 
From: "wouter meeussen" <wouter.meeussen at pandora.be>
To: <ham>; "math-fun" <math-fun at mailman.xmission.com>; "Seqfan (E-mail)" 
<seqfan at ext.jussieu.fr>
Cc: <scotth at ichips.intel.com>; <rgwv at rgwv.com>
Sent: Saturday, May 07, 2005 6:46 AM
Subject: Re: [math-fun] better posed problem? (small progress)


> about:
> A103306 Triangle read by rows: T(n,k) = number of k-subsets of the n-th 
> roots of 1 that add to zero
> (0 <= k <= n).
> and:
> A103314 Total number of subsets of the n-th roots of 1 that add to zero.
>
> Hi all,
> the closest approach to sanity ;-) in this matter was Scott's result 
> below. He came to
>>>   #(30) = 146854
> with the proviso that
>>> More precisely, I find at least that many zero sum subsets.  I 
>>> conjecture
>>> that's all the zero sum subsets, but I don't have a proof.
>
> So I undertook to reconstruct row n=30 of A103306 and found confirmation:
> T[30,k=0..30]= 146854;
> {1,0,15,10,105,126,525,780,2055,3060,5955,8010,12285,14190,17715,17190}
>
> I'll put the table at 
> http://users.pandora.be/Wouter.Meeussen/RootZeros.xls
> It's still incomplete for n=26, 27 and 28. I'll complete those in due 
> time.
>
> Together with Neil, I can only hope that someone comes up with a full & 
> fast calculation technique
> for this nifty(?) problem.
>
> Wouter.