Generalizing the Wythoff Array and other Fibonacci Facts to Tribonacci Numbers

TL;DR

This paper extends known Fibonacci properties to the Tribonacci sequence, introducing the Trithoff array and 13 new related sequences, thereby broadening the understanding of Fibonacci-like structures.

Contribution

It generalizes Fibonacci facts to Tribonacci numbers, creating the Trithoff array and identifying 13 new sequences, a novel extension of previous work.

Findings

Introduction of the Trithoff array

13 new Tribonacci-related sequences

Generalization of Fibonacci properties to Tribonacci numbers

Abstract

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.