I'm 16!

A function $F(x,y,z)$ is known to have $F(1,1,1) = 1, F(2,1,1) = 4, F(2,2,1) = 8, F(2,2,2) = 173$ . Find the sum of all the values of $c$ satisfying

$\displaystyle \left \lfloor {\nabla}_{5\textbf{i} + 9\textbf{j} + c\textbf{k}} F \right \rfloor = 16$

Note

Directional Derivative is found approximately.