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A192714 Number of 13X2 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 13 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations) 1

%I #5 Mar 31 2012 12:36:20

%S 2,6,19,55,140,331,732,1533,3055,5857,10824,19386,33743,57293,95044,

%T 154445,246197,385697,594416,902641,1351643,1998191,2918046,4213843,

%U 6019994,8515367,11930845,16568416,22815114,31168260,42253487,56871045

%N Number of 13X2 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 13 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)

%C Column (13,2,n) of A192710

%H R. H. Hardin, <a href="/A192714/b192714.txt">Table of n, a(n) for n = 1..62</a>

%e Some solutions for 13X2 <= 2*4^2

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

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

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

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

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

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

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

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

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

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

%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0

%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0

%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 07 2011

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)