Tribonacci multiplication

Arithmetics on number systems with irrational bases

For irrational β > 1 we consider the set Fin(β) of real numbers for which |x| has a finite number of non-zero digits in its expansion in base β. In particular, we consider the set of β-integers, i.e. numbers whose β-expansion is of the form ∑n i=0 xiβ , n ≥ 0. We discuss some necessary and some sufficient conditions for Fin(β) to be a ring. We also describe methods to estimate the number of fra...

Addition and Multiplication of Beta-Expansions in Generalized Tribonacci Base

We study properties of β-numeration systems, where β > 1 is the real root of the polynomial x −mx − x−1, m ∈ N, m ≥ 1. We consider arithmetic operations on the set of β-integers, i.e., on the set of numbers whose greedy expansion in base β has no fractional part. We show that the number of fractional digits arising under addition of β-integers is at most 5 for m ≥ 3 and 6 for m = 2, whereas und...

More Identities On The Tribonacci Numbers

In this paper, we use a simple method to derive di¤erent recurrence relations on the Tribonacci numbers and their sums. By using the companion matrices and generating matrices, we get more identities on the Tribonacci numbers and their sums, which are more general than that given in literature [E. Kilic, Tribonacci Sequences with Certain Indices and Their Sum, Ars Combinatoria 86 (2008), 13-22....

Tribonacci Sequences With Certain Indices And Their Sums

In this paper, we derive new recurrence relations and generating matrices for the sums of usual Tribonacci numbers and 4n subscripted Tribonacci sequences, fT4ng ; and their sums. We obtain explicit formulas and combinatorial representations for the sums of terms of these sequences. Finally we represent relationships between these sequences and permanents of certain matrices. 1. Introduction Th...

Tribonacci and Tribonacci-Lucas Numbers via the Determinants of Special Matrices