A192710 T(i,j,k) = Number of i X j 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*k^2 (number of sets of i zero-sum j-vectors with total modulus squared not more than 2*k^2, ignoring vector and component permutations), 3d array by constant coordinate sum planes: (((T(i+1,j+1,s-i-j+1), j=0..s-i), i=0..s), s=0..infinity).

1, 1, 2, 1, 1, 3, 2, 1, 2, 1, 1, 4, 5, 2, 1, 4, 2, 1, 2, 1, 1, 5, 8, 6, 2, 1, 7, 8, 2, 1, 5, 2, 1, 2, 1, 1, 6, 13, 15, 8, 2, 1, 10, 20, 11, 2, 1, 10, 9, 2, 1, 6, 2, 1, 2, 1, 1, 7, 18, 26, 21, 9, 2, 1, 15, 54, 48, 13, 2, 1, 16, 36, 13, 2, 1, 12, 10, 2, 1, 6, 2, 1, 2, 1, 1, 8, 25, 45, 48, 28, 9, 2, 1, 20, 104

Offset: 1

Author

R. H. Hardin Jul 07 2011

Keywords

• nonn
• tabf

Examples

			Some solutions for n=245, T(3,4,6)
.-3..1..1..1...-5..0..0..5...-5..0..2..3...-4..1..1..2...-5.-1..3..3
.-2.-2..1..3...-2.-1..1..2...-3.-1..2..2...-2.-2..0..4...-1.-1.-1..3
.-2.-1.-1..4...-2..0..1..1...-2.-2..2..2...-2.-1..1..2...-1.-1.-1..3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1640

Crossrefs

Column T(1,3,n) is A000982(n+1).

Column T(2,2,n) is A036702(n).