 Combined with the use of generating functions, this technique is able to count many polyominoes at once, thus enabling it to run many times faster than methods that have to generate every polyomino.Although it has excellent running time, the tradeoff is that this algorithm uses exponential amounts of memory (many gigabytes of memory are needed for "n" above 50), is much harder to program than the other methods, and can't currently be used to count free polyominoes.Theoretical arguments and numerical calculations support the estimate for the number of fixed polyominoes of size n

where "λ" = 4.0626 and "c" = 0.3169.