  Hofstadter's Q-sequence remains an enigma fifty years after its introduction.
Initially, the terms of the sequence increase monotonically by 0 or 1 at a
time. But, Q(12)=8 while Q(11)=6, and monotonicity fails shortly thereafter. In
this paper, we add a third term to Hofstadter's recurrence, giving the
recurrence B(n)=B(n-B(n-1))+B(n-B(n-2))+B(n-B(n-3)). We show that this
recurrence, along with a suitable initial condition that naturally generalizes
Hofstadter's initial condition, generates a sequence whose terms all increase
monotonically by 0 or 1 at a time. Furthermore, we give a complete description
of the resulting frequency sequence, which allows the nth term of our sequence
to be efficiently computed. We conclude by showing that our sequence cannot be
easily generalized.
