cp's OEIS Frontend

A192705 Number of 5X2 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 5 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192705 #7 Jun 02 2025 04:13:14
%S A192705 2,6,14,29,56,101,166,267,407,604,865,1211,1659,2236,2956,3861,4949,
%T A192705 6299,7906,9849,12120,14817,17958,21641,25859,30753,36318,42732,49917,
%U A192705 58116,67296,77693,89219,102175,116527,132515,150117,169602,191013,214662
%N A192705 Number of 5X2 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 5 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192705 Column (5,2,n) of A192710
%H A192705 R. H. Hardin, <a href="/A192705/b192705.txt">Table of n, a(n) for n = 1..200</a>
%e A192705 Some solutions for 5X2 <= 2*4^2
%e A192705 .-3..3...-2..2...-2..2...-1..1...-1..1...-2..2...-3..3...-3..3...-3..3...-2..2
%e A192705 .-1..1...-1..1...-2..2...-1..1...-1..1...-2..2...-1..1....0..0...-1..1...-2..2
%e A192705 .-1..1...-1..1...-1..1....0..0...-1..1...-2..2...-1..1....0..0....0..0...-2..2
%e A192705 .-1..1....0..0...-1..1....0..0....0..0...-2..2...-1..1....0..0....0..0....0..0
%e A192705 .-1..1....0..0...-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%K A192705 nonn
%O A192705 1,1
%A A192705 _R. H. Hardin_ Jul 07 2011