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A192707 Number of 7X2 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 7 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations) 1

%I

%S 2,6,17,39,85,167,309,546,919,1486,2338,3564,5300,7703,11016,15451,

%T 21303,28978,38908,51626,67686,87827,112967,144076,182028,228322,

%U 284414,351962,432504,528554,642212,776430,933563,1117263,1331217,1579771,1865945

%N Number of 7X2 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 7 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)

%C Column (7,2,n) of A192710

%H R. H. Hardin, <a href="/A192707/b192707.txt">Table of n, a(n) for n = 1..163</a>

%e Some solutions for 7X2 <= 2*4^2

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

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

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

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

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

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

%e ..0..0....0..0....0..0....0..0....0..0...-1..1....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 January 21 06:26 EST 2022. Contains 350473 sequences. (Running on oeis4.)