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Generalizing the Wythoff Array and other Fibonacci Facts to Tribonacci Numbers

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arxiv 2211.01410 v1 pith:UFPGWIIN submitted 2022-11-02 math.NT

Eric Chen , Adam Ge , Andrew Kalashnikov , Tanya Khovanova , Ella Kim , Evin Liang , Mira Lubashev , Matthew Qian
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Rohith Raghavan Benjamin Taycher Samuel Wang
This is my paper · ORCID
classification math.NT
keywords arrayfibonaccitribonaccifactssequencetextitwythoffalex
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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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