Generalizing the Wythoff Array and other Fibonacci Facts to Tribonacci Numbers

Eric Chen, Adam Ge,Andrew Kalashnikov,Tanya Khovanova,Ella Kim,Evin Liang, Mira Lubashev,Matthew Qian,Rohith Raghavan,Benjamin Taycher, Samuel Wang

arxiv（2022）

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摘要

In this paper, we generalize a lot of facts from John Conway and Alex Ryba's paper, \textit{The extra Fibonacci series and the Empire State Building}, where we replace the Fibonacci sequence with the Tribonacci sequence. We study the Tribonacci array, which we also call \textit{the Trithoff array} to emphasize the connection to the Wythoff array. We describe 13 new sequences.

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