2006 Canadian MO Problems/Problem 1


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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See also

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