A192702 Number of 3X3 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 3 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

2, 9, 36, 114, 308, 745, 1597, 3194, 5944, 10408, 17408, 28207, 43739, 66091, 97417, 139756, 197048, 273225, 370834, 497159, 658332, 859295, 1109567, 1420234, 1795384, 2253449, 2806737, 3464221, 4246712, 5179322, 6262896, 7537671, 9025226

Offset: 1

Author

R. H. Hardin Jul 07 2011

Keywords

• nonn

Comments

Column (3,3,n) of A192710

Examples

			Some solutions for 3X3 <= 2*4^2
.-2.-2..4...-2..0..2...-1.-1..2...-3..0..3...-2..0..2...-4..2..2...-2.-1..3
.-1.-1..2...-2..0..2...-1.-1..2...-2.-1..3...-1.-1..2...-1..0..1...-1.-1..2
.-1..0..1...-2..0..2...-1.-1..2....0..0..0...-1.-1..2....0..0..0...-1.-1..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..128