Unique factorial design or number sequence

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Fayyaz on 24 Nov 2017
Commented: Fayyaz on 24 Nov 2017
Hi,
How would I be able to generate a unique sequence by combining [4 6 8 10 12] and [1 2 3], like the ones below:
4 4 4 4 4 1
4 4 4 4 4 2
4 4 4 4 4 3
4 4 4 4 6 1
4 4 4 4 6 2
4 4 4 4 6 3
. . .. . . . .
12 12 12 12 12 1
12 12 12 12 12 2
12 12 12 12 12 3
However, I do not need repetitions, e.g., I need only one sequence 6 8 8 8 8 1 and NOT 8 6 8 8 8 1

Andrei Bobrov on 24 Nov 2017
Edited: Andrei Bobrov on 24 Nov 2017
v1 = [4 6 8 10 12];
v2 = [1 2 3];
n1 = length(v1);
n2 = length(v2);
ii = flip(fullfact([n2,n1*ones(1,n1)]),2);
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))];
or without fullfact:
c = {1:n1,1:n2};
ii = cell(1,numel(v1)+1);
[ii{end:-1:1}] = ndgrid(c{[2,ones(1,n1)]});
ii = cell2mat(cellfun(@(x)x(:),ii,'un',0));
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))'];
EDIT
Fayyaz on 24 Nov 2017
Many thanks. That is working perfectly :)

Image Analyst on 24 Nov 2017
Here's one way:
v1 = [4 6 8 10 12]
v2 = [1 2 3]
n1 = length(v1)
n2 = length(v2)
row = 1;
output = zeros(n1^5*n2, n1+1);
for k1 = 1 : n1
for k2 = 1 : n1
for k3 = 1 : n1
for k4 = 1 : n1
for k5 = 1 : n1
for k6 = 1 : n2
vec = [v1(k1), v1(k2), v1(k3), v1(k4), v1(k5), v2(k6)];
output(row, :) = vec;
row = row + 1;
end
end
end
end
end
end
% Print to command window:
output

mounika on 24 Nov 2017
a = [4 6 8 10 12];
b= [1 2 3];
c = ones(1,6); % initialize to ones
t = randi([1,5],1,1); % to randomly pick a number from 'a'
z = randi([1,3],1,1); % to randomly pick a number from 'a'
c = c.*a(t);
c(:,end) = b(z); % assign the end value with any no of b
disp(c);
This gives numbers like: 10 10 10 10 10 2 8 8 8 8 8 3 2 2 2 2 2 1 ...
I didn't really understand the last part of your question ' However, I do not need repetitions, e.g., I need only one sequence 6 8 8 8 8 1 and NOT 8 6 8 8 8 1'
You can change the above code for your specifications.