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

[David Wilson]

Sorry, the element in question is A103314(30) = 120214.  Though incorrect, 
this
element occurs much earlier in the sequence than I thought, and maybe we
should wait for a verdict before truncating the sequence.  I have reason to 
think
that all the other elements are correct.

Also, it seems like A103314(4k) is always a square.  Is there a good reason
for this to be true?

----- Original Message ----- 
From: "David Wilson" <davidwwilson at comcast.net>
To: <ham>; "wouter meeussen" <wouter.meeussen at pandora.be>; "Seqfan (E-mail)" 
<seqfan at ext.jussieu.fr>
Cc: "Neil Sloane" <njas at research.att.com>
Sent: Sunday, May 08, 2005 12:09 AM
Subject: Re: [math-fun] better posed problem? (small progress)


> 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.
>