Combinations with a condition

I have 4 vectors as shown below. I want to create a matrix that list all the possible combinations with the condition that

x = [0 1 2 3 4 5 6]
x1 = [0 3 6]
x2 = [0 3 6]
x3 = [0 3 6]

Answer 1

[John D'Errico]

Easy enough.

x = 0:6;
[x1,x2,x3] = ndgrid([0 3 6]);
x123 = [x1(:),x2(:),x3(:)];
ind = ismember(sum(x123,2),3*x);

x123(ind,:)

ans = 27×3

0 0 0 3 0 0 6 0 0 0 3 0 3 3 0 6 3 0 0 6 0 3 6 0 6 6 0 0 0 3

You want to be careful that you work in INTEGER arithmetic though. This is why I multiplied x by 3, instead of dividing the sum by 3.

[Nicolas Leport]

Thanks, how do I add the corresponding x value to that matrix?