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A192713 Number of 12X2 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 12 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192713 #7 Jun 02 2025 04:13:51
%S A192713 2,6,19,53,133,310,669,1371,2684,5037,9125,16021,27343,45523,74103,
%T A192713 118121,184828,284258,430192,641623,944008,1371445,1968786,2795325,
%U A192713 3927604,5465114,7534219,10297413,13958709,18775675,25067921,33235421
%N A192713 Number of 12X2 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 12 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192713 Column (12,2,n) of A192710
%H A192713 R. H. Hardin, <a href="/A192713/b192713.txt">Table of n, a(n) for n = 1..65</a>
%e A192713 Some solutions for 12X2 <= 2*4^2
%e A192713 .-2..2...-2..2...-2..2...-1..1...-2..2...-2..2...-1..1....0..0...-2..2...-1..1
%e A192713 .-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1....0..0...-1..1...-1..1
%e A192713 .-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1....0..0...-1..1....0..0
%e A192713 .-1..1...-1..1...-1..1...-1..1...-1..1....0..0...-1..1....0..0...-1..1....0..0
%e A192713 ..0..0...-1..1...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
%e A192713 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1....0..0
%K A192713 nonn
%O A192713 1,1
%A A192713 _R. H. Hardin_ Jul 07 2011