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 $ ?

You could write
$$
\sum_{i=1}^{3} f(2i-1).
$$
Otherwise it is allowed to write
$$
\sum_{1 \leq i\leq 5, i \text{ odd}} f(i).
$$
(Here in your example $f(i) = i^2$ of course).
So in general whatever condition you have on the index, you can write that underneath the sum. In general you will find some people prefer one thing over another.
