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A192714 Number of 13X2 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 13 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192714 #7 Jun 02 2025 04:14:01
%S A192714 2,6,19,55,140,331,732,1533,3055,5857,10824,19386,33743,57293,95044,
%T A192714 154445,246197,385697,594416,902641,1351643,1998191,2918046,4213843,
%U A192714 6019994,8515367,11930845,16568416,22815114,31168260,42253487,56871045
%N A192714 Number of 13X2 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 13 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192714 Column (13,2,n) of A192710
%H A192714 R. H. Hardin, <a href="/A192714/b192714.txt">Table of n, a(n) for n = 1..62</a>
%e A192714 Some solutions for 13X2 <= 2*4^2
%e A192714 .-3..3...-2..2...-2..2...-2..2...-2..2...-2..2...-3..3...-2..2...-2..2...-3..3
%e A192714 .-1..1....0..0...-2..2...-2..2...-2..2...-2..2...-1..1...-1..1...-1..1...-2..2
%e A192714 .-1..1....0..0...-1..1...-2..2...-2..2....0..0...-1..1...-1..1...-1..1...-1..1
%e A192714 .-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1...-1..1
%e A192714 .-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0
%e A192714 .-1..1....0..0...-1..1...-1..1....0..0....0..0...-1..1...-1..1...-1..1....0..0
%e A192714 .-1..1....0..0...-1..1...-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0
%e A192714 ..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1...-1..1....0..0
%e A192714 ..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1....0..0....0..0
%e A192714 ..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1....0..0....0..0
%e A192714 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192714 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192714 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%K A192714 nonn
%O A192714 1,1
%A A192714 _R. H. Hardin_ Jul 07 2011