This is ugly and untested, but it's what came to mind.

/^([a-z])(?!.*\1)  # letter, never followed by the same letter
  ([a-z])(?!.*\2)  # another
  ([a-z])(?=(?!\3).(?!\3).\3(?!.*\3))    # letter followed by two othe
+rs, then itself and never again
  ([a-z])(?!.*\4)  # another of the first type
  ([a-z])(?!.*\5)  # another
  \3               # the repeated char
  ([a-z])(?!\6)    # another unique char
  ([a-z])\z        # final char
/x;
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(update: changed ?: to ?=)