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Tag for the usage of RSolve, RecurrenceTable, DifferenceRoot, and other functions related to difference equations.
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RSolve and a recurrence relation
In the book An Introduction to the Analysis of Algorithms there is a recurrence relation for the number of compares used in Quicksort algorithm:
$$ C_N=N+1+\sum_{0≤k≤N-1}\frac{1}{N}(C_k+C_{N−k−1}) $$
…