Hilbert-Waring Theorem/Sequence

Sequence
The integer sequence of values of $g \left({k}\right)$ begins:
 * $1, 4, 9, 19, 37, 73, 143, 279, 548, 1079, 2132, 4223, 8384, 16673, 33203, 66190, 132055, \ldots$