Brilliant!
My solution was very memory inefficient. This is great!

Would anyone care to explain this implementation a little bit?
I am not quite sure if I follow along the last three if statements.
Why would x2 bet set to 2 * h[++i]?

same question here

Length of an array is a public final int, so no calculation is done.

see here

http://docs.oracle.com/javase/specs/jls/se7/html/jls-10.html#jls-10.7

really?learn it!

That is not true.

i<length

and

i<arr.length

have exactly the same cost.

The difference would be, when comparing to collection size, such as ArrayList and using .size() method, but here it doesn't matter.

for (int i=0; i<arr.length; i++)

Calculate the length in the cycle, is not efficient

int sum = 0;
int length = arr.length;
for (int i=0; i<length; i++) {
sum += (i % 2 == 0) ? arr[i] : arr[i] * arr[i];
}
return sum;

Much too easy for a 5kyu, at least in Python...

Translated to Java. Please approve when you have the chance :D

Title is not that relevant. It is a good kata, but title needs to be changed to give a better idea of what the kata is about. Try to leave out political opinions.

I actually wrote it out using sumation notation and then simplified down.

Ugh, why didn't I see the pattern when I did this? :(

How much honor is earned for kata translations?