# 2. (15p) We shall consider a function A, defined by the recurrences A(0,n n+1 for n...

###### Question:

2. (15p) We shall consider a function A, defined by the recurrences A(0,n n+1 for n 20 for m>0 for m, n > 0 A(m, n) A(m-1, A(m, n-1)) = Observe that A(1,1) = A(0,A(1,0))=A(0,2) = 3 A(1,2 A(0, A(1, 1)) A(0,34 and it is now not hard to see (as can be proved by an easy induction) that A(1,n)n 2 for all n 20 1. (5p) Calculate A(2,0), A(2,1), A(2,2), and A(2,3) Then state (you are not required to prove) a general formula for A(2,n).

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