Journal of Integer Sequences, Vol. 28 (2025), Article 25.5.4

Generalizing the Wythoff Array and Other Fibonacci Facts to Tribonacci Numbers


Eric Chen, Adam Ge, Andrew Kalashnikov, Ella Kim, Evin Liang, Mira Lubashev, Matthew Qian, Rohith Raghavan, Benjamin Taycher, and Samuel Wang
PRIMES STEP
Department of Mathematics
MIT
77 Massachusetts Ave.
Cambridge, MA 02139
USA

Tanya Khovanova
Department of Mathematics
MIT
77 Massachusetts Ave.
Cambridge, MA 02139
USA

Abstract:

In this paper, we generalize many facts from a recent paper of Conway and Ryba, where we replace the Fibonacci sequence in that paper with the Tribonacci sequence. We study the Tribonacci array, which we also call the Trithoff array to emphasize the connection to the Wythoff array. We also describe 13 new sequences.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000045 A000073 A000201 A000213 A001590 A001950 A003144 A003145 A003146 A003265 A003714 A003726 A003849 A020992 A060140 A100683 A104449 A136175 A214899 A269725 A269726 A300867 A305373 A351631 A351685 A351689 A352719 A352748 A353083 A353084 A353086 A353090 A353178 A353193 A354215 A356823.)

Received June 26 2024; revised versions received May 21 2025; August 9 2025. Published in Journal of Integer Sequences, September 18 2025.

Return to Journal of Integer Sequences home page