  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.
