MathDB
f(n,k): f(n,0)=f(n,n)=1 and f(n,k)=f(n-1,k-1)+f(n-1,k) for 0<k<n , f(3991,1993)

Source: Mexican Mathematical Olympiad 1993 OMM P4

July 29, 2018
number theoryfunctionrecursive

Problem Statement

f(n,k)f(n,k) is defined by (1) f(n,0)=f(n,n)=1f(n,0) = f(n,n) = 1 and (2) f(n,k)=f(n−1,k−1)+f(n−1,k)f(n,k) = f(n-1,k-1) + f(n-1,k) for 0<k<n0 < k < n. How many times do we need to use (2) to find f(3991,1993)f(3991,1993)?
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