Why does Householder tridiagonalization cost $4n^3/3$?

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In Golub, Van Loan - Matrix Computations page 459, it says

This algorithm requires 4n^3/3 flops when symmetry is exploited in calculating the rank- 2 update.

But I don't quite understand that. How is the symmetry exploited and why is the cost 4n^3/3?

Can anyone prove it in more detail? Thanks!