A192703 - OEIS

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 #5 Mar 31 2012 12:36:20

%S 2,6,12,23,41,70,106,159,230,323,436,578,757,975,1232,1536,1889,2317,

%T 2797,3355,3994,4711,5523,6438,7465,8618,9888,11296,12839,14557,16398,

%U 18449,20689,23115,25758,28591,31673,34995,38586,42415,46528,50984,55687

%N 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 Column (4,2,n) of A192710

%H R. H. Hardin, <a href="/A192703/b192703.txt">Table of n, a(n) for n = 1..200</a>

%e Some solutions for 4X2 <= 2*4^2

%e .-3..3...-3..3...-1..1...-2..2...-3..3...-2..2...-2..2...-1..1...-1..1...-2..2

%e ..0..0...-1..1...-1..1...-2..2...-2..2...-2..2....0..0...-1..1...-1..1...-2..2

%e ..0..0...-1..1....0..0....0..0...-1..1...-2..2....0..0...-1..1...-1..1...-2..2

%e ..0..0....0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0...-2..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 07 2011