Sigma notation only for odd iterations $ \sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55 $
How to write this Sigma notation only for odd numbers: $ 1^2+3^2+5^2 = 35 $ ?

Just use the following for any $f(i)$:
$$\sum_{i=0}^n f(2i+1)$$
Edit: Sorry, I somehow mistook the question for "even".
