The Numbers of Distinct Squares and Cubes in the Tribonacci Sequence

2016/05/15 by Huang, Yuke, Wen, Zhiying
#11B85 #68Q45 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04503

Abstract

The Tribonacci sequence \mathbbT is the fixed point of the substitution σ(a,b,c)=(ab,ac,a). In this note, we give the explicit expressions of the numbers of distinct squares and cubes in \mathbbT[1,n] (the prefix of \mathbbT of length n).

Related

• The numbers of distinct and repeated squares and cubes in the Tribonacci sequence
• The numbers of powers in the Tribonacci sequence
• The Square Trees in the Tribonacci Sequence
• The number of distinct and repeated squares and cubes in the Fibonacci sequence
• Mechanical Proofs of Properties of the Tribonacci Word