# rabbit sequence

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## rabbit sequence

[′ab·ət ′sē·kwəns]
(mathematics)
A sequence of binary numbers that is recursively generated by the rules 0→1 (young rabbits grow old) and 1→10 (old rabbits stay old and beget young ones); beginning with a single 1, successive generations are 1, 10, 101, 10110, 10110101, and so forth.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
They show that Hopcroft's algorithm has a worst case behavior for the automata recognizing Fibonacci words.
We prove that the same holds for all standard Sturmian words having an ultimately periodic directive sequence (the directive sequence for Fibonacci words is (1, 1, ...)).
(2007), Castiglione, Restivo and Sciortino replace the de Bruijn words by Fibonacci words. They show that, for this word, there is no more choice in Hopcroft's algorithm, and that the unique execution of Hopcroft's algorithm runs in time [OMEGA](n log n).
The case of Fibonacci words corresponds the directive sequence (1, 1, ...).
Example 1 (Fibonacci) For d = (1, 1, ...) = ([bar.1]), one gets [s.sub.n+1] = [s.sub.n][s.sub.n-1] for n [greater than or equal to] 1, and the standard words generated by d are the Fibonacci words 1, 0, 01, 010, 01001, ...
(2007) in the case of the Fibonacci words, with directive sequence d = ([bar.1]).
There are two types of Fibonacci words, "natural" and "arbitrary".
"Natural Fibonacci words" are composed of the letters of adjacent numbers in Fibonacci's series.
But it is of most interest because of the sacred aura surrounding the notion of the sum total of all "FIBONACCI WORDS"!
"Arbitrary Fibonacci words" are slightly more interesting.
Counting Dave's, this brings the total to a cool fifty-two Fibonacci words (Why cool?
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