Question on overlapping generations
Is that derivation for $k(t+1)$ correct? Technically, you never reach the steady state, but only asimptotically as $t\rightarrow\infty$, but at infinity the $A(t)$ will also be infinite because it grows exponentially with time. I suspect that $k(t+1)$ should depend on $(1+g)$ instead of $A(t)$.
Usually these models are expressed in units of effective labor, that is, dividing the capital stock $K(t)$ and the labor $L(t)$ (and hence, the production and consumption) by $N(t)$ and $A(t)$.