From 3Blue1Brown.

A lesson on generating functions, and clever uses of complex numbers for counting
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Special thanks: https://3b1b.co/lessons/subsets-puzzle#thanks

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/2022/06/generating-functions-3b1b.html
https://youtu.be/9SzwfM-S9sk

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
https://youtu.be/sD0NjbwqlYw

Fourier series
https://youtu.be/r6sGWTCMz2k

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

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These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:
https://github.com/3b1b/videos/

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

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

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Website: https://www.3blue1brown.com