cp's OEIS Frontend

A192702 Number of 3X3 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 3 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192702 #7 Jun 02 2025 04:12:59
%S A192702 2,9,36,114,308,745,1597,3194,5944,10408,17408,28207,43739,66091,
%T A192702 97417,139756,197048,273225,370834,497159,658332,859295,1109567,
%U A192702 1420234,1795384,2253449,2806737,3464221,4246712,5179322,6262896,7537671,9025226
%N A192702 Number of 3X3 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 3 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192702 Column (3,3,n) of A192710
%H A192702 R. H. Hardin, <a href="/A192702/b192702.txt">Table of n, a(n) for n = 1..128</a>
%e A192702 Some solutions for 3X3 <= 2*4^2
%e A192702 .-2.-2..4...-2..0..2...-1.-1..2...-3..0..3...-2..0..2...-4..2..2...-2.-1..3
%e A192702 .-1.-1..2...-2..0..2...-1.-1..2...-2.-1..3...-1.-1..2...-1..0..1...-1.-1..2
%e A192702 .-1..0..1...-2..0..2...-1.-1..2....0..0..0...-1.-1..2....0..0..0...-1.-1..2
%K A192702 nonn
%O A192702 1,1
%A A192702 _R. H. Hardin_ Jul 07 2011