Results 11 to 20 of about 2,369,502 (88)
Binomial Transform of the Generalized Tribonacci Sequence
Asian Research Journal of Mathematics, 2020 In this paper, we define the binomial transform of the generalized Tribonacci sequence and as special cases, the binomial transform of the Tribonacci, Tribonacci-Lucas, Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas and adjusted Tribonacci-Lucas sequences will be introduced. We investigate their properties in details.
Y¨uksel Soykan
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On Sum Formulas for Generalized Tribonacci Sequence
Journal of Scientific Research and Reports, 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 sequences.
Yüksel Soykan
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On Four Special Cases of Generalized Tribonacci Sequence: Tribonacci-Perrin, modified Tribonacci, modified TribonacciLucas and adjusted Tribonacci-Lucas Sequences [PDF]
, 2020 In this paper, we investigate four new special cases, namely, Tribonacci-Perrin, modified Tribonacci, modified Tribonacci-Lucas, adjusted Tribonacci-Lucas sequences, of the generalized Tribonacci sequences. We present Binet’s formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Soykan, Yüksel
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Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers [PDF]
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014 Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degree n, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and ...
Juan Li +3 more
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A Complete Categorization of When Generalized Tribonacci Sequences Can Be Avoided by Additive Partitions [PDF]
The Electronic Journal of Combinatorics, 2000 A set or sequence $U$ in the natural numbers is defined to be avoidable if ${\bf N}$ can be partitioned into two sets $A$ and $B$ such that no element of $U$ is the sum of two distinct elements of $A$ or of two distinct elements of $B$. In 1980, Hoggatt [5] studied the Tribonacci sequence $T=\{t_n\}$ where $t_1=1$, $t_2=1$, $t_3=2$, and $t_n=t_{n-1}+t_{
Mike Develin
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On the higher power sums of reciprocal higher-order sequences. [PDF]
ScientificWorldJournal, 2014 Let {un} be a higher‐order linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higher‐order sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.
Wu Z, Zhang J.
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Gaussian Generalized Tribonacci Numbers [PDF]
, 2018 In this paper, we define Gaussian generalized Tribonacci numbers and as special cases, we investigate Gaussian Tribonacci and Gaussian Tribonacci-Lucas numbers with their properties.
Okumuş, İnci +3 more
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On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v, k = 0, 1, 2, ⋯, where l=lk is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces ℓpL,c0L, and
Taja Yaying +4 more
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Dold sequences, periodic points, and dynamics
Bulletin of the London Mathematical Society, Volume 53, Issue 5, Page 1263-1298, October 2021., 2021 Abstract In this survey we describe how the so‐called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Jakub Byszewski +2 more
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Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
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