# Questions tagged [recurrences]

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### Reference for "trick" on guessing solutions to quadratic recurrences with differential equations

Consider the recurrence $$g(h) = g(h-1) - \frac{1}{4}g(h-1)^2,$$ for $h \geq 0$ and $g(0)=1$. This recurrence occurs in many applications (For example fast minimum cut algorithms, the Galton-Watson ...
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### Urn model and recursion

We have an urn with $n$ white balls. In each iteration we pick a ball at random. If it's white, we paint it red and return it to the urn. If it's already red, we discard it. We lose the game if (after ...
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### A surprising result with the Riccati difference equation

I was looking at the Riccati difference equation with positive and negative indices $$R_n=\frac{aR_{n-1}+b}{cR_{n-1}+d}\quad n\in[0,N]\\ R_n=\frac{-dR_{n+1}+b}{cR_{n+1}-a}\quad n\in[-N,0]\\$$ along ...
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