A192710 - OEIS

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).

%I #7 Aug 31 2019 15:53:28

%S 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,

%T 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,

%U 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

%N 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).

%H R. H. Hardin, <a href="/A192710/b192710.txt">Table of n, a(n) for n = 1..1640</a>

%e Some solutions for n=245, T(3,4,6)

%e .-3..1..1..1...-5..0..0..5...-5..0..2..3...-4..1..1..2...-5.-1..3..3

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

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

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

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

%K nonn,tabf

%O 1,3

%A _R. H. Hardin_ Jul 07 2011