2006 Canadian MO Problems/Problem 1

Problem

Let $f(n,k)$ be the number of ways distributing $k$ candies to $n$ children so that each child receives at most two candies. For example, $f(3,7)=0$ , $f(3,6)=1$ , and $f(3,4)=6$ . Evaluate $f(2006,1)+f(2006,4)+f(2006,7)+\dots+f(2006,1003)$ .

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2006 Canadian MO (Problems)
Preceded by First question	1 • 2 • 3 • 4 • 5	Followed by Problem 2