cp's OEIS Frontend

A192704 Number of 4X3 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 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192704 #7 Jun 02 2025 04:13:09
%S A192704 2,10,45,191,639,1925,5059,12197,27061,55957,109220,204227,361922,
%T A192704 621790,1032797,1662821,2607574,4007507,5999290,8835971,12784870,
%U A192704 18186200,25491781,35326689,48192368,65114102,87009836,115061673,150717188
%N A192704 Number of 4X3 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 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192704 Column (4,3,n) of A192710
%H A192704 R. H. Hardin, <a href="/A192704/b192704.txt">Table of n, a(n) for n = 1..63</a>
%e A192704 Some solutions for 4X3 <= 2*4^2
%e A192704 .-2..1..1...-2..0..2...-2..0..2...-3..1..2...-3..1..2...-3..1..2...-3..0..3
%e A192704 .-2..1..1...-2..1..1...-2..0..2...-2..0..2...-1.-1..2...-3..1..2...-2..0..2
%e A192704 .-2..1..1...-1.-1..2...-1.-1..2...-1.-1..2...-1.-1..2....0..0..0...-2..1..1
%e A192704 .-2..1..1...-1.-1..2....0..0..0...-1..0..1....0..0..0....0..0..0....0..0..0
%K A192704 nonn
%O A192704 1,1
%A A192704 _R. H. Hardin_ Jul 07 2011