Vectorized summation for vectorized indices

Hi, I need to write a code for the following summation. Thanks in advance.

Where k=1,2,3...... For example if one considers upto the summation becomes

where each and run as 1,2,3....... The second term of the summation indicates: for example if the values of =1 and =1 the terms inside the summation become . Here i and j run as 1,2,3......

[Dyuman Joshi]

What have you tried yet?

[Rajesh]

I could not be able to generalize. I just took two indices and and wrote code but I need to generalize for all indices. My code is given below

for i=1:1:100

for j=1:1:100

sum1=0;

for =1:1:20

for =1:1:20

sum1=sum1+X(i,,,j)-X(i,+1,+1,j);

end

end

end

end

[Dyuman Joshi]

What is X?

And I hope you realise that you are overwriting the variable sum1 with every iteration of the 2nd for loop without storing the values in any other variables.

[Rajesh]

I understand your query but I don't need to store that. This is small portion of a big code. Ultimately, I need to use RK4 to solve the X. I'm generating those elements just by the above summation. If I get help to generalize the above summation for (with or without storing will not effect), my job is done.