How does this recurrence relation simplify?
$X_n$ = $X_{n-1}$ + $2pqX_{n-1}$ - $qX_{n-1}$
It seems like some kind of binomial expansion but I am not sure.
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2If you really meant $X_n=(1+2pq-q)X_{n-1}$ then that's simply a geometric progression. – dxiv Apr 22 '17 at 01:44