better posed problem?

[wouter meeussen]

of all k-subsets (including the empty subset) of the n-th roots of 1, say n= 0 to 20, 0>= k>=n, how
many add to zero?

1, 1, 2, 2, 4, 2, 10, 2, 16, 8, 34, 2, 100, 2, 130, 38, 256, 2, 1000, 2, 1156 ...

{1}
{1, 0},
{1, 0, 1},
{1, 0, 0, 1},
{1, 0, 2, 0, 1},
{1, 0, 0, 0, 0, 1},
{1, 0, 3, 2, 3, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 4, 0, 6, 0, 4, 0, 1},
{1, 0, 0, 3, 0, 0, 3, 0, 0, 1},
{1, 0, 5, 0, 10, 2, 10, 0, 5, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 6, 4, 15, 12, 24, 12, 15, 4, 6, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 7, 0, 21, 0, 35, 2, 35, 0, 21, 0, 7, 0, 1},
{1, 0, 0, 5, 0, 3, 10, 0, 0, 10, 3, 0, 5, 0, 0, 1},
{1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 9, 6, 36, 36, 96, 90, 162, 128, 162, 90, 96, 36, 36, 6, 9, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 10, 0, 45, 4, 120, 20, 210, 40, 256, 40, 210, 20, 120, 4, 45, 0, 10, 0, 1}}

?? it feels funny to take the empty subset of the zero'th (?) roots of 1.
Superseek comes up empty handed on the rowsum 2,2,4,2,10,...,1156

Thanks to Daniel Asimov, Franklin T. Adams-Watters and Mike Speciner for their kind tutoring.
Will submit to OEIS unless anyone still sees bugs.

W.

----- Original Message -----
From: "wouter meeussen" <wouter.meeussen at pandora.be>
To: "Seqfan (E-mail)" <seqfan at ext.jussieu.fr>; "math-fun" <math-fun at mailman.xmission.com>
Sent: Friday, March 11, 2005 11:21 PM
Subject: well posed problem?


of all subsets of the n-th roots of -1, n= 1 to 20, how many add to zero?
??
0, 1, 1, 3, 1, 6, 1, 11, 4, 8, 1, 50, 1, 10, 9, 107, 1, 240, 1, 316
??
where are the 'groupies' when you need them?

W.