Matrix in Romberg method

Hi! I´ve been asked to create a code that works with the Romberg Integration method, I´ve tried to create a matrix that displays the procedure, so to speak, but I can´t seem to be able to create it. I´m still new to Matlab so I wanted to ask for some help on how to do it. Thanks in advance :)

Here´s my code

li = -3;
ls = 3;
k = 4;
n = 2.^(0:k-1);
i = [0:1:n(k)];
% disp(i([1:n+1])
f =@(xi) (log(4*(xi.^2)+4));
arr = [];

for c = 1:k
    difx = (ls - li)./n([1:k]);
    xi = li + (i([1:n(c)+1]).*difx(c));
    a = numel(xi);
    sum1 = [f(xi(1))  2.*f(xi(2:a-1))  f(xi(a))];
    est = (difx(c)/2)*(sum(sum1));
    arr = [arr est];
end
%Here´s the start of the actual method and my attempt at the matrix
val = arr
fun =@ (z,y) (((4.^(z-1)).*val((2:k),y)-val((1:k-1),y))./((4.^(z-1))-1));
for y = 1:k
    for x = 1:3
        z = [2:1:k]
        fil = fun(z,y)
        nuz = k - [k-1:-1:1]
        filz = zeros(1,nuz);
        val = [val; fil filz]
    end
end
disp(arr)