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A192706 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).

%I A192706 #7 Jun 02 2025 04:13:19
%S A192706 2,6,16,34,71,135,235,396,641,993,1496,2193,3136,4398,6065,8214,10949,
%T A192706 14438,18760,24151,30736,38755,48448,60129,73970,90426,109793,132568,
%U A192706 158991,189853,225331,266394,313294,367015,428094,497667,575969,664608
%N A192706 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 A192706 Column (6,2,n) of A192710
%H A192706 R. H. Hardin, <a href="/A192706/b192706.txt">Table of n, a(n) for n = 1..200</a>
%e A192706 Some solutions for 6X2 <= 2*4^2
%e A192706 .-2..2...-3..3...-1..1...-1..1...-2..2...-2..2...-3..3...-3..3...-1..1...-1..1
%e A192706 .-2..2...-2..2...-1..1...-1..1...-1..1...-2..2....0..0...-1..1...-1..1....0..0
%e A192706 .-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1....0..0
%e A192706 ..0..0....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0...-1..1....0..0
%e A192706 ..0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192706 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%K A192706 nonn
%O A192706 1,1
%A A192706 _R. H. Hardin_ Jul 07 2011