For quadratic hashing, i.e an open-addressed table with the hash function of the form -
$h(x, i)= (h'(x) + c_1i + c_2i^2) \mod m$
Setting $c_1 = c_2 = 1/2$, and $m$ to some power of 2, leads to a hash function
$h(x, i) = (h'(x) + 1 + 2 + ... +i) \mod m$
I have read that the load-factor of a quadratically probed table should not exceed $0.5$ to guarantee insertion to succeed if an empty cell exists in the table. Wikipedia's article here https://en.wikipedia.org/wiki/Quadratic_probing#Limitations says that
"With the exception of the triangular number case for a power-of-two-sized hash table, there is no guarantee of finding an empty cell once the table gets more than half full, or even before the table gets half full if the table size is not prime. "
So what is the maximum load factor that will guarantee successful insertion for this case?