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Number of 6X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 6 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)
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%I #5 Mar 31 2012 12:36:20

%S 2,6,16,34,71,135,235,396,641,993,1496,2193,3136,4398,6065,8214,10949,

%T 14438,18760,24151,30736,38755,48448,60129,73970,90426,109793,132568,

%U 158991,189853,225331,266394,313294,367015,428094,497667,575969,664608

%N Number of 6X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 6 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)

%C Column (6,2,n) of A192710

%H R. H. Hardin, <a href="/A192706/b192706.txt">Table of n, a(n) for n = 1..200</a>

%e Some solutions for 6X2 <= 2*4^2

%e .-2..2...-3..3...-1..1...-1..1...-2..2...-2..2...-3..3...-3..3...-1..1...-1..1

%e .-2..2...-2..2...-1..1...-1..1...-1..1...-2..2....0..0...-1..1...-1..1....0..0

%e .-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1....0..0

%e ..0..0....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0...-1..1....0..0

%e ..0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0

%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 07 2011