Catalan Unrank

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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 .


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.


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



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