Adding elements with specific distance 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

Answer 1

[Andrei Bobrov]

t =[1   2   3   3   1   2   2   1   3
   3   2   1   1   3   2   2   3   1];

s = size(t);
M = reshape(t,s(1),3,[]);
i3 = nchoosek(1:3,2);
X = sum(reshape(M(:,:,i3(end:-1:1,:)),s(1),3,2,[]),3);
out = reshape(X(:,:,:,end:-1:1),s(1),[]);