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A192712 Number of 11X2 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 11 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

%I A192712 #7 Jun 02 2025 04:13:45
%S A192712 2,6,19,51,126,285,604,1208,2310,4237,7513,12885,21536,35072,55893,
%T A192712 87271,133793,201572,299171,437546,631447,900231,1268643,1768448,
%U A192712 2440754,3336495,4520239,6073339,8095214,10708816,14066591,18351402,23788458
%N A192712 Number of 11X2 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 11 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C A192712 Column (11,2,n) of A192710
%H A192712 R. H. Hardin, <a href="/A192712/b192712.txt">Table of n, a(n) for n = 1..75</a>
%e A192712 Some solutions for 11X2 <= 2*4^2
%e A192712 .-1..1...-3..3...-3..3...-3..3...-2..2...-1..1...-2..2...-3..3...-2..2...-3..3
%e A192712 ..0..0...-2..2...-1..1...-2..2...-2..2...-1..1...-1..1...-1..1...-2..2...-1..1
%e A192712 ..0..0...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1
%e A192712 ..0..0...-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0
%e A192712 ..0..0....0..0...-1..1...-1..1...-1..1....0..0...-1..1....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%e A192712 ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
%K A192712 nonn
%O A192712 1,1
%A A192712 _R. H. Hardin_ Jul 07 2011