Calculating a matrix from other matrices

How can I write the following matrix?

M = [C*B; 
     C*A*B + C*B;     
     C*A^2*B + C*A*B + C*B;
               .      
               .      
               .      
     C*A^(N-1)*B + C*A^(N-2)*B + ... + C*B];

A, B, and C are 2D arrays with size(A)=(n,n), size(B)=(n,p), and size(C)=(q,n). N is a positive integer.

[Walter Roberson]

I posted code for the 2D version of this a couple of years ago, where the values were being copied down the diagonals.

Unfortunately it has been far too long for me to recall the key words that would needed to find it within my other posts :(

Answer 1

[Matt J]

Q=eye(n);
Mcell=cell(n,1);

for i=1:N
    
    Mcell{i}=C*Q*B;
    
    Q=A*Q+Q;
    
end

M=cell2mat(Mcell);

[Saleh Msaddi]

Thanks @Matt J for your answer. However, I tried to execute the code and compre the results but they are not the same (only the first 2 rows are the same)

N = 4;

A = rand(4);
B = rand(4,1);
C = rand(1,4);
[n,p] = size(B);

R = [C*B;
     C*A*B + C*B;
     C*A^2*B + C*A*B + C*B;
     C*A^3*B + C*A^2*B + C*A*B + C*B];
 
Q=eye(n);
Mcell=cell(n,1);
for i=1:N
    
    Mcell{i}=C*Q*B;
    
    Q=A*Q+Q;
    
end
M=cell2mat(Mcell);

R == M

[Matt J]

Sorry, it should be

N = 4;

A = rand(4);
B = rand(4,1);
C = rand(1,4);
[n,p] = size(B);

R = [C*B;
     C*A*B + C*B;
     C*A^2*B + C*A*B + C*B;
     C*A^3*B + C*A^2*B + C*A*B + C*B];
 
[Q,Q0]=deal(eye(n));
Mcell=cell(n,1);
for i=1:N
    
    Mcell{i}=C*Q*B;
    
    Q=A*Q+Q0;
    
end
M=cell2mat(Mcell);

difference=norm(R-M)

difference = 1.8310e-15