Results 41 to 50 of about 263 (131)
On Partial Sum of Tribonacci Numbers [PDF]
, 2020 We study the sum ( , ) = ∑ =0 + of step apart Tribonacci numbers for any 1 ≤ ≤ . We prove that ( , ) satisfies certain −3 + with integers , , , and
Jiin Jo, Eunmi Choi
core
, 2008 summary:Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus $p$ and by its powers $p^t$, which were deduced by M. E. Waddill.
Klaška, Jiří
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Minimal weight expansions in Pisot bases
Journal of Mathematical Cryptology, 2008 For applications to cryptography, it is important to represent numbers with a small number of non-zero digits (Hamming weight) or with small absolute sum of digits.
Frougny Christiane, Steiner Wolfgang
doaj +1 more source
Earthline Journal of Mathematical Sciences, 2022 In this paper, we introduce a new operator defined in this paper, we give some new generating functions of binary products of Tribonacci and Tribonacci Lucas polynomials and special numbers.
Hind Merzouk +2 more
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Solutions of the Markoff equation in Tribonacci numbers
, 2023 In this paper, we determine all of the positive integer solutions of the so-called Markoff equation x2 + y2 + z2 = 3xyz in the sequence of Tribonacci numbers {Tn}, i.e.
Hashim, Hayder R., Hayder R. Hashim
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Identities involving the tribonacci numbers squared via tiling with combs
, 2022 The number of ways to tile an $n$-board (an $n\times1$ rectangular board) with $(\frac12,\frac12;1)$-, $(\frac12,\frac12;2)$-, and $(\frac12,\frac12;3)$-combs is $T_{n+2}^2$ where $T_n$ is the $n$th tribonacci number.
Allen, Michael A., Edwards, Kenneth
core
Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences
, 2020 In the paper, the authors present several explicit formulas for the $(p,q,r)$-Tribonacci polynomials and generalized Tribonacci sequences in terms of the Hessenberg determinants and, consequently, derive several explicit formulas for the Tribonacci ...
Wei Shih Du, Can Kizilates, Feng Qi
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, 2021 In this paper, closed forms of the sum formulas ∑_{k=0}ⁿkx^{k}W_{k}², ∑_{k=0}ⁿkx^{k}W_{k+2}W_{k} and ∑_{k=0ⁿkx^{k}W_{k+1}W_{k} for the squares of generalized Tribonacci numbers are presented.
Yüksel SOYKAN, SOYKAN, Yüksel
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On Sum Formulas for Generalized Tribonacci Sequence
, 2020 In this paper, closed forms of the sum formulas for generalized Tribonacci numbers are presented. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third-order linear recurrance ...
Yüksel Soykan
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Incomplete tribonacci numbers and polynomials
, 2020 We define the incomplete tribonacci sequence of numbers and polynomials. We study recurrence relations, some properties of these numbers and polynomials, and the generating function of the incomplete tribonacci ...
José L Ramírez, Víctor F Sirvent
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