Initializing live version
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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 .[more]
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.[less]
Contributed by: Ed Pegg Jr (August 2022)
Open content licensed under CC BY-NC-SA