Lucas Number Circular Tilings (synthwave enumeration)
This synthwave enumeration shows all the tilings of a circular grid divided into n pieces from n = 1 to n = 11 using tiles that cover one or two cells. Can you tell the pattern? Can you prove why or how the Lucas numbers appear? If you are looking for more information about this, I recommend the wonderful textbook Proofs that Really Count: The Art of Combinatorial Proof from Arthur Benjamin and Jennifer Quinn: https://bookstore.ams.org/dol-27
If you enjoy this enumeration, check out a Fibonacci tiling video : • Fibonacci domino tilings of (2 x n)-grid (...
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