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The skew of a binary string is the difference between the number of zeroesand the number of ones, while the length of the string is the sum of these twonumbers. We consider certain suffixes of the lexicographically-least de Bruijnsequence at natural breakpoints of the binary string. We show that the skew andlength of these suffixes are enumerated by sequences generalizing the Fibonacciand Lucas numbers, respectively.

Generalized Fibonacci recurrences and the lex-least De Bruijn sequence