On the roots of the cubic defining the Tribonacci sequences

2002/09/20 by Mario Catalani, Catalani, Mario
Mathematics · #11B37 #11B39 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:11B37 #msc:11B39

paper · pdf · doi:10.48550/arxiv.math/0209265

arxiv created 2002/09/20 · arxiv updated 2009/11/30

Abstract

We consider a sequence of sums of powers of the the roots of the cubic equation characterizing the Tribonacci sequences and derive its relationship with a particular Tribonacci sequence. Then we make a conjecture on the possible generalization.

Related

• The numbers of powers in the Tribonacci sequence
• Identities for Tribonacci-related sequences
• The Numbers of Distinct Squares and Cubes in the Tribonacci Sequence
• Bifurcating Continued Fractions
• The numbers of distinct and repeated squares and cubes in the Tribonacci sequence