add elements in a matrix

I have a matrix like this

1 2 3 3 1 2 2 1 3

3 2 1 1 3 2 2 3 1

What i want to do is a 3x9 matrix that contains this

cell (1,1) . (1 + 3 + 2) - 1 .... 1(the first element) + 3(the fourth element) + 2(the 7th element) - 1(my initial cell)

cell (1,2) . (2 + 1 + 1) - 2 .... 2(the second element) + 1(the fifth element) + 1(the 8th element) - 2(my initial cell)

and so on... cell (1,5) . (1 + 2 + 1)-1 .... 1(the 5th element) + 2(2nd element) + 1(8th element) - 1(initial cell)

It's like calculating the total of all the numbers where the indices are separated by 3

output =

5 2 5 3 3 6 4 3 5

3 6 3 5 5 2 4 5 3

I have this code

    for k1 = 1:2
    for k2 = 1:3
        S(k1,k2) = sum(a(k1,3+k2:3:end),2);
    end
end
  but it adds the first 3 number only, i want it to continue till the end of the matrix

Answer 1

[Azzi Abdelmalek]

A=[1 2 3 3 1 2 2 1 3;3 2 1 1 3 2 2 3 1];
ff=numel(A(1,1:3:end))-1;
[n,m]=size(A);
[ii,jj]=ndgrid(1:n,1:m);
AA=[A A];
out=arrayfun(@(x,y) sum(AA(x,y+3:3:y+ff*3)),ii,jj)