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Number of 1X8 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 1 zero-sum 8-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 2,10,42,147,415,1040,2336,4841,9324,17035,29556,49428,79553,124531,

%T 189360,281680,409383,584737,819889,1133021,1541844,2072913,2751299,

%U 3615478,4697427,6051068,7720384,9776322,12276825,15316939,18967552

%N Number of 1X8 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 1 zero-sum 8-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)

%C Column (1,8,n) of A192710

%H R. H. Hardin, <a href="/A192695/b192695.txt">Table of n, a(n) for n = 1..90</a>

%e Some solutions for 1X8 <= 2*4^2

%e .-4.-1..0..0..1..1..1..2...-3.-1.-1.-1..0..0..3..3...-3.-3.-1..0..1..2..2..2

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 07 2011