How to find the minimum sum and the corresponding index by iterations?

I need to determine the minimum value and the corresponding index when it is achieved according to the equation that divides the time series by two parts:

In this equation, n1 and n2 are the sizes of the two parts of the time series which constitute the original time series of the size n. The following additional conditions are set to the equation: the minimum size of the first part of the time series is set to be n1 = 10 for which n2 = n – n1, and then the size is increased: n1 = 11, 12,…, k, where k = n – 10 at which n2 = 10.

I have tried to program this equation to find the minimum sum by iterations, but I am not sure that the script is correct. In particular, are the loops correctly applied? Also, it seems like n2=11 here at the end, but it has to be 10 when the iterations finish.

n=66; % The size of the original time series for the characteristic Y (e.g., temperature)
n1=n-20; % This operation is needed for the loops below
minsum=10000000; % Declaration of the variable needed for the "if" operator at the end of the script. 
for j=1:n1
    ik=10+j-1;  % This is from 10 to 55
    s31=0; % This is preallocation

for i=1:ik  % This is from 1 to 10, 11,...,55
        s31=s31+Y(i); % The values are taken from 1 to 10,11,...,55

        cn=ik; % This is from 10 to 55
Mean1=s31/cn; % Finding of the means from 1 to 10,11,...,55. So, the minimum size of the sample over which the mean is found is 10 years
s32=0; 
s32=s32+(Y(i)-Mean1).^2; % This is the first term of the equation 

s41=0;
in1=ik+1; % This is from 11 to 56
for k=in1:n % This is from 11 to 66
s41=s41+Y(k);

mn=n-in1+1; % This is from 56 to 11
Mean2=s41/mn; % Finding of the means from 66 to 11,12,...,56 or from 11,12,...,56 to 66 to be consistent with the notation in the formula. So, the minimum size of the sample over which the mean is found is 11 years
s42=0; 
s42=s42+(Y(k)-Mean2).^2; % This is the second term of the equation


summation=s32+s42; % Finding the sums between all possible sizes of the two parts of the time series


if summation<minsum 
minsum=summation % The minimum sum is displayed in the last output among the iterated values. 

imin=in1 % Finding the index in the original time series for which the minimum sum is achieved. 
end
end
end
end