Editing Fibonacci coding (section)

==Generalizations==
The Fibonacci encodings for the positive integers are binary strings that end with "11" and contain no other instances of "11".  This can be generalized to binary strings that end with ''N'' consecutive 1s and contain no other instances of ''N'' consecutive 1s.  For instance, for ''N''&nbsp;=&nbsp;3 the positive integers are encoded as 111, 0111, 00111, 10111, 000111, 100111, 010111, 110111, 0000111, 1000111, 0100111, ….  In this case, the number of encodings as a function of string length is given by the sequence of [[tribonacci number]]s.

For general constraints defining which symbols are allowed after a given symbol, the maximal information rate can be obtained by first finding the optimal transition probabilities using a [[maximal entropy random walk]], then using an [[entropy coder]] (with switched encoder and decoder) to encode a message as a sequence of symbols fulfilling the found optimal transition probabilities.