The question asks to:construct a DFA which accepts exactly $\frac{n(n-1)(n-2)}{6} + \frac{n(n-1)}{2}+1$ many members of $\{0, 1\}^n$ for every n.I have no idea where to start to constructing the DFA, could you give some directions?By the way, how many states should this DFA have?
Construct a deterministic finite automation
automata;finite automata