Undergrad Enumerate all 1-state Turing Machines

[cobalt124]

Hi, using the definition of a TM from https://en.wikipedia.org/wiki/Busy_beaver a 1-state TM would have:

one "operational" state a, plus the Halt State h
a tape alphabet of 0,1
a tape initially all zeros
Given this the possible 5-tuples a 1-state TM transition table could have are:

(current state,current symbol,symbol to write,direction of shift,next state)

(a,0,0,L,a)
(a,0,0,L,h)
(a,0,0,R,a)
(a,0,0,R,h)
(a,0,1,L,a)
(a,0,1,L,h)
(a,0,1,R,a)
(a,0,1,R,h)
(a,1,0,L,a)
(a,1,0,L,h)
(a,1,0,R,a)
(a,1,0,R,h)
(a,1,1,L,a)
(a,1,1,L,h)
(a,1,1,R,a)
(a,1,1,R,h)

The Wikipedia article states that there are (4n + 4)^2n n-state Turing machines meeting this definition. For n=1 that means 64. How does the above definition result in 64 1-state TMs?

 

[cobalt124]

It's OK I think I've worked it out. Each TM has a transition table with two 5-tuples, one with inputs a,0 and one with inputs a,1 in all possible combinations giving a total of 64 TMs.