x = [-1,4,1,4,2];
n = length(x);
y = zeros(1,2*n-1);
z = xcorr(x);
for delay = -n+1:n-1
    if delay<0
        y(delay+n) = sum(x(1:n+delay).^x(-delay+1:n));
    elseif delay==0
        y(delay+n) = sum(x.^2);
    else
        y(delay+n) = sum(x(delay+1:n).^x(1:n-delay));
    end
end

subplot(3,1,1);
stem(x);
title('General Function');

subplot(3,1,2);
stem(z);
title('Auto-correlation with Correlation Function');

subplot(3,1,3);
stem(-n+1:n-1,y);
title('Auto-correlation Manually');