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A192699 Number of 2X4 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 2 zero-sum 4-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192699 #7 Jun 02 2025 04:12:43
%S A192699 2,11,48,166,459,1125,2426,4871,9028,15919,26530,42795,66234,100066,
%T A192699 146708,211012,295903,409009,555042,743702,980297,1279677,1648401,
%U A192699 2106146,2660304,3336122,4142715,5114735,6259510,7619959,9210010
%N A192699 Number of 2X4 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 2 zero-sum 4-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192699 Column (2,4,n) of A192710
%H A192699 R. H. Hardin, <a href="/A192699/b192699.txt">Table of n, a(n) for n = 1..120</a>
%e A192699 Some solutions for 2X4 <= 2*4^2
%e A192699 .-3.-1..1..3...-3.-1..2..2...-1.-1..0..2...-2.-1..0..3...-2.-2..1..3
%e A192699 .-3..1..1..1...-2.-1..0..3....0..0..0..0...-2..0..0..2...-2..0..0..2
%K A192699 nonn
%O A192699 1,1
%A A192699 _R. H. Hardin_ Jul 07 2011