The set of sequences of length n ending in HH (and with no earlier HH) and beginning with a T are in bijection with the set of sequences of length n-1 ending in HH (and with no earlier HH) by the bijection

   def f(s):
     assert(s[0] == 'T')
     return s[1:]

whose inverse is

  def f_inverse(s):
    return 'T' + s