The   Fibonacci Word   may be created in a manner analogous to the   Fibonacci Sequence   as described here:

    Define   F_Word1   as   1
    Define   F_Word2   as   0
    Form     F_Word3   as   F_Word2     concatenated with   F_Word1    i.e.:   01
    Form     F_Wordn   as   F_Wordn-1   concatenated with   F_wordn-2



Task

Perform the above steps for     n = 37.

You may display the first few but not the larger values of   n.

{Doing so will get the task's author into trouble with them what be (again!).} 

Instead, create a table for   F_Words   1   to   37   which shows:

   The number of characters in the word
   The word's Entropy


Related tasks
 
   Fibonacci word/fractal
   Entropy
   Entropy/Narcissist


entropy = (p - 1) Log[2, 1 - p] - p Log[2, p];
 
TableForm[
 Table[{k, Fibonacci[k], 
   Quiet@Check[N[entropy /. {p -> Fibonacci[k - 1]/Fibonacci[k]}, 15],
      0]}, {k, 37}], 
 TableHeadings -> {None, {"N", "Length", "Entropy"}}]