We consider the sequence 2n(n - 1/2 - rho(2n)), where rho(2n) is the P
erron value of the Brualdi-Li matrix of order 2n. We prove that the se
quence converges, find its limit, and show that asymptotically, the se
quence is monotonically decreasing. In particular, this addresses some
problems raised by Friedland and Katz.