Olympiad level counting (Generating functions)

A lesson on generating functions, and clever uses of complex numbers for counting
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Artwork by Kurt Burns
Music by Vince Rubinetti

Nice writeup and video giving solutions to the exercises at the end, by Benjamin Hackl
https://benjamin-hackl.at/blog/2022/0...
   • Solutions to 3b1b's generating function ex...  

102 Combinatorial problems, by Titu Andreescu and Zuming Feng
https://amzn.to/3wAPoNq

Generatingfunctionology by Herbert Wilf
https://amzn.to/3sPJ8Al

Visualizing the Riemann zeta function
   • But what is the Riemann zeta function? Vis...  

Fourier series
   • But what is a Fourier series?  From heat f...  

Timestamps
0:00 - Puzzle statement and motivation
4:31 - Simpler example
6:51 - The generating function
11:52 - Evaluation tricks
17:24 - Roots of unity
26:31 - Recap and final trick
30:13 - Takeaways

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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https://github.com/ManimCommunity/manim/

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Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

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