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A192715 Number of 14X2 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 14 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192715 #7 Jun 02 2025 04:14:06
%S A192715 2,6,19,56,146,350,790,1685,3421,6680,12575,22923,40636,70228,118550,
%T A192715 196038,317911,506487,793842,1225546,1865180,2802329,4157823,6098617,
%U A192715 8848923,12709523,18076665,25480353,35605456,49349547,67866426,92643950
%N A192715 Number of 14X2 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 14 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192715 Column (14,2,n) of A192710
%H A192715 R. H. Hardin, <a href="/A192715/b192715.txt">Table of n, a(n) for n = 1..56</a>
%e A192715 Some solutions for 14X2 <= 2*4^2
%e A192715 .-2..2...-3..3...-3..3...-2..2...-2..2...-2..2...-3..3...-3..3...-1..1...-1..1
%e A192715 .-1..1...-1..1...-1..1...-2..2...-2..2...-1..1...-2..2...-1..1...-1..1...-1..1
%e A192715 .-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0...-1..1...-1..1...-1..1...-1..1....0..0....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0...-1..1...-1..1....0..0...-1..1....0..0....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0...-1..1....0..0....0..0...-1..1....0..0....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1...-1..1
%e A192715 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
%e A192715 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
%e A192715 .-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192715 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192715 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192715 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%K A192715 nonn
%O A192715 1,1
%A A192715 _R. H. Hardin_ Jul 07 2011