Find the recurrence relation satisfied by Sn, where Sn is the number of regions into which three dimensional space is divided by n planes if every three of the planes meet in one point, but no four of the planes go through the same point. I figured out that the nth plane should go through every two from the set of n-1 planes, however, I don't get how many regions that adds. It's difficult to visualise this.
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2@JeanMarie The formula for $P_n$ there is not very revealing, it's nicer to write it as $\binom{n}{0}+\binom{n}{1}+\binom{n}{2}+\binom{n}{3}$. – Alexander Burstein Mar 27 '24 at 07:27
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@Alexander Burstein You are right, as in the answers here by Calvin Lin and also Guojun Zhang – Jean Marie Mar 27 '24 at 07:46
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@JeanMarie Thanks, it looks like it does. – Andii Koo Mar 27 '24 at 09:26