Is there any standard notation for turing machines outcomes?

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On 2 symbols 1-state turning machine, there are 64 posible machines taking into account their transition tables. One of this machines could be: $$A0:0LA$$ $$A1:0RH$$

(meaning: in state A, reading a 0, write 0, goes left and transition to A, in state A, reading a 1, write 0, goes right and halt.)

Another one could be: $$A0:1RA$$ $$A1:0RA$$

Another one: $$A0:1LH$$ $$A1:0RA$$

Assuming we start with a blank tape, only the last one halts. The first just keep going left, and the second just goes right writing 1's.

On 2 symbols 1-state machines, there are 64 posible machines (if we consider transition tables as they source code). But if we consider their behaviour there are only 8 possible outcomes.

  1. Going Left: $(0L)*$
  2. Going Right: $(0R)*$
  3. Going Left writing 1's: $(1L)*$
  4. Going Right writing 1's: $(1R)*$
  5. Go left and halt: $0LH$
  6. Write 1,go left and halt: $1LH$
  7. Go right and halt: $RH$
  8. Write 1, go right and halt: $1RH$

(Only the last 4, halt)

For 2 symbols n-state machines:

  • The formula for calculating how many machines in terms of transition tables are $(2*2*2*(n+1))^n$? My rational: 2 read symbols, 2 write symbols, 2 directions, (n+1) next states to be defined (independently) in n (running) states
  • Is there some kind of standard notation for outcomes?
  • Is there a formula for calculating outcomes?

For 2 symbols 2-state machines:

  • There are 1296 machines (if my previous formula is ok), but how many outcomes?
  • It is known how many of this 1296 halts?