Create a matrix where every row adds to a number and within the matrix represents every possibility of the row combinations

Hi,

I am looking to make a matix with "n" columns and have each row add up to "k" which is a positive interger. The number of rows will be dictated by the requirement that every combination of possible rows is included in the matrix. If I use n=4 and k=3, it takes 20 rows to include every combination of rows where each adds up to k=3. Example matrix below:

I'm hoping to write some code that will take arbitrary values of n and k and output such a matrix.

3 0 0 0

2 1 0 0

2 0 1 0

2 0 0 1

1 2 0 0

1 1 1 0

1 1 0 1

1 0 2 0

1 0 1 1

1 0 0 2

0 3 0 0

0 2 1 0

0 2 0 1

0 1 2 0

0 1 1 1

0 1 0 2

0 0 3 0

0 0 2 1

0 0 1 2

0 0 0 3

Answer 1

[Matt J]

See attached.

n=4;k=3;
diophantine(ones(1,n),k,0:k)

ans = 20×4

3 0 0 0 2 1 0 0 1 2 0 0 0 3 0 0 2 0 1 0 1 1 1 0 0 2 1 0 1 0 2 0 0 1 2 0 0 0 3 0

Answer 2

[Bruno Luong]

A non recursive engine AllVL1 in FEX

>> allVL1(4,3)

ans =

     0     0     0     3
     0     0     1     2
     0     0     2     1
     0     0     3     0
     0     1     0     2
     0     1     1     1
     0     1     2     0
     0     2     0     1
     0     2     1     0
     0     3     0     0
     1     0     0     2
     1     0     1     1
     1     0     2     0
     1     1     0     1
     1     1     1     0
     1     2     0     0
     2     0     0     1
     2     0     1     0
     2     1     0     0
     3     0     0     0