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Aug
30

Catalan Numbers

Recently I was trying to count the number of n-bit numbers that have an equal number of 1′s and 0′s.  For example, there are 6 such numbers for 4-bit long numbers (0011, 0101, 0110, 1001, 1010, 1100).  I wrote a simple program to count such numbers for arbitrarily long numbers.  However, the program was computationally [...]