Generalizing the Wythoff Array and other Fibonacci Facts to Tribonacci Numbers

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