cp's OEIS Frontend

A192703 Number of 4X2 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 4 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192703 #7 Jun 02 2025 04:13:04
%S A192703 2,6,12,23,41,70,106,159,230,323,436,578,757,975,1232,1536,1889,2317,
%T A192703 2797,3355,3994,4711,5523,6438,7465,8618,9888,11296,12839,14557,16398,
%U A192703 18449,20689,23115,25758,28591,31673,34995,38586,42415,46528,50984,55687
%N A192703 Number of 4X2 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 4 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192703 Column (4,2,n) of A192710
%H A192703 R. H. Hardin, <a href="/A192703/b192703.txt">Table of n, a(n) for n = 1..200</a>
%e A192703 Some solutions for 4X2 <= 2*4^2
%e A192703 .-3..3...-3..3...-1..1...-2..2...-3..3...-2..2...-2..2...-1..1...-1..1...-2..2
%e A192703 ..0..0...-1..1...-1..1...-2..2...-2..2...-2..2....0..0...-1..1...-1..1...-2..2
%e A192703 ..0..0...-1..1....0..0....0..0...-1..1...-2..2....0..0...-1..1...-1..1...-2..2
%e A192703 ..0..0....0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0...-2..2
%K A192703 nonn
%O A192703 1,1
%A A192703 _R. H. Hardin_ Jul 07 2011