# Possible number of DFAs, NFAs, DPDAs, NPDAs, NDTMs and DTMs for various input parameters

I came across problem asking for possilble number of DFAs for a given number of states and alphabet. I started guessing if we can find possible number different automatas for given number of states, input alphabet and stack alphabet etc.

Given,
$$Q$$ is set of states
$$Σ$$ is input alphabet
$$Γ$$ is stack alphabet for PDAs and tape alphabet for TMs
$$L$$ means move head to left in TM
$$R$$ means move head to right in TM
$$ϵ$$ is empty symbol

I came up with following table: First $$Q$$ in each cell of "Possible number of machines" column is possible number of start states. Last $$2^Q$$ is possible combinations of final states. And remaining middle part is number of transition. combinations. Also I have used the symbols directly to denote number of elements in each set. For example, $$Q$$ is set of states, but I used $$Q$$ to denote number of states.

Am I correct with these counts?

PS: this is combinatorial problem in the context of automata theory.