Given $n$ and $k$ two positive integers we begin with an urn that contains $kn$ white balls. We then proceed through $n$ turns where on each turn $k$ black balls are added to the urn and then $2k$ random balls are removed from the urn.
We let $B_t(n,k)$ be the number of black balls that are removed on turn $t$.
Further define $E(n,k)$ as the expectation of $\displaystyle \sum_{t=1}^n B_t(n,k)^2$.
You are given $E(2,2) = 9.6$.
Find $E(10^6,10)$. Round your answer to the nearest whole number.
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