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A binary sequence is called totally balanced if the number of zeros is at least as large as the number of ones as you traverse , and the total counts are equal. If has length , this implies and .

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For ones there are totally balanced binary sequences, where is the th Catalan number.

The sorted list of balanced binary sequences for starts with 00001111 and ends with 01010101.

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Contributed by: Ed Pegg Jr (August 2022)
Open content licensed under CC BY-NC-SA

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