a) Consider the sequence (Si)iN, where s; is the number of bistrings of length i that contain three consecutive Os. Define this sequence recursively. b) Consider the sequence (ti)ieN, where t; is the number of bistrings of length i that contain the string 01. Define this sequence recursively. c) Consider the sequence (ui)iezt, where u; is the number of messages that can be transmitted in i microseconds using three different signals: one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal. Define this sequence recursively.