Mathegoras

Sequences and series › Recursive sequences › Computing terms of a recurrence

Evaluating the Ackermann function

High school · ●●○○○ 20 pts

Define a function A(m,n)A(m, n) by A(m,n)={n+1if m=0,A(m−1,1)if m>0 and n=0,A(m−1,A(m,n−1))if m>0 and n>0.A(m,n) = \begin{cases} n+1 & \text{if } m = 0, \\ A(m-1, 1) & \text{if } m > 0 \text{ and } n = 0, \\ A(m-1, A(m, n-1)) & \text{if } m > 0 \text{ and } n > 0. \end{cases} Compute A(2,1)A(2, 1).

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recurrence relationsfunction iteration