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%I #7 Sep 04 2022 20:55:03
%S 2,6,19,49,118,259,534,1042,1941,3465,5996,10040,16364,26012,40522,
%T 61835,92657,136556,198316,283977,401349,560438,774140,1058263,
%U 1432174,1920672,2554179,3369134,4409927,5730887,7397192,9486111,12090252,15318436
%N Number of 10 X 2 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 10 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
%C Column (10,2,n) of A192710.
%H R. H. Hardin, <a href="/A192711/b192711.txt">Table of n, a(n) for n = 1..86</a>
%e Some solutions for 10 X 2 <= 2*4^2
%e .-2..2...-3..3...-2..2...-1..1....0..0...-2..2...-3..3...-1..1...-3..3...-2..2
%e .-1..1...-2..2...-2..2...-1..1....0..0...-2..2...-2..2....0..0...-1..1...-1..1
%e .-1..1...-1..1...-2..2...-1..1....0..0...-2..2...-1..1....0..0....0..0...-1..1
%e .-1..1...-1..1...-1..1....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1
%e ..0..0...-1..1....0..0....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1
%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
%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
%Y Cf. A192710.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jul 07 2011