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A192709 Number of 9X2 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 9 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192709 #7 Jun 02 2025 04:13:40
%S A192709 2,6,19,46,108,231,460,872,1581,2737,4607,7508,11904,18426,27989,
%T A192709 41631,60856,87536,124153,173696,239976,327657,442880,592595,785351,
%U A192709 1031659,1344609,1738831,2232241,2845802,3605355,4538949,5681318,7071215,8756412
%N A192709 Number of 9X2 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 9 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192709 Column (9,2,n) of A192710
%H A192709 R. H. Hardin, <a href="/A192709/b192709.txt">Table of n, a(n) for n = 1..102</a>
%e A192709 Some solutions for 9X2 <= 2*4^2
%e A192709 .-2..2...-3..3...-2..2...-2..2...-1..1...-2..2...-2..2....0..0...-3..3...-1..1
%e A192709 .-1..1...-2..2...-2..2...-2..2...-1..1...-1..1...-1..1....0..0...-2..2...-1..1
%e A192709 .-1..1...-1..1...-2..2...-2..2...-1..1...-1..1...-1..1....0..0...-1..1...-1..1
%e A192709 .-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1....0..0...-1..1...-1..1
%e A192709 .-1..1...-1..1....0..0...-1..1....0..0...-1..1...-1..1....0..0....0..0...-1..1
%e A192709 .-1..1....0..0....0..0...-1..1....0..0....0..0...-1..1....0..0....0..0...-1..1
%e A192709 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
%e A192709 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
%e A192709 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
%K A192709 nonn
%O A192709 1,1
%A A192709 _R. H. Hardin_ Jul 07 2011