Results 21 to 30 of about 105 (79)
Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse ...
Li Liu, Zhaolin Jiang, Zidong Wang
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, 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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On Partial Sum of Tribonacci Numbers
International Journal of Mathematics and Mathematical Sciences, Volume 2015, Issue 1, 2015., 2015 We study the sum st(k,r)=∑i=0tTki+r of k step apart Tribonacci numbers for any 1 ≤ r ≤ k. We prove that st(k,r) satisfies certain Tribonacci rule st(k,r)=akst-1(k,r)+bkst-2(k,r)+st-3(k,r)+λ with integers ak, bk, ck, and λ.
Eunmi Choi, Jiin Jo, Nawab Hussain
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Total Graph Interpretation of the Numbers of the Fibonacci Type
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We give a total graph interpretation of the numbers of the Fibonacci type. This graph interpretation relates to an edge colouring by monochromatic paths in graphs. We will show that it works for almost all numbers of the Fibonacci type. Moreover, we give the lower bound and the upper bound for the number of all (A1, 2A1)‐edge colourings in trees.
Urszula Bednarz +3 more
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Tribonacci modulo $2^t$ and $11^t$ [PDF]
, 2008 summary:Our previous research was devoted to the problem of determining the primitive periods of the sequences $(G_n\mod p^t)_{n=1}^{\infty }$ where $(G_n)_{n=1}^{\infty }$ is a Tribonacci sequence defined by an arbitrary triple of integers. The solution
Klaška, Jiří
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Integer Semigroups Associated with Dumont‐Thomas Numeration Systems
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 Given a primitive substitution, we define different binary operations on infinite subsets of the nonnegative integers. These binary operations are defined with the help of the Dumont‐Thomas numeration system; that is, a numeration system associated with the substitution. We give conditions for these semigroups to have an identity element.
Víctor F. Sirvent +5 more
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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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Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 The row first‐minus‐last right (RFMLR) circulant matrix and row last‐minus‐first left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the exact formulae of determinants of the two pattern matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas sequences in terms of
Zhaolin Jiang +3 more
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Journal of Applied Mathematics, Volume 2012, Issue 1, 2012., 2012 Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well‐known property which states the (i, j) entry of Am (A is adjacency matrix) is equal to the number of ...
Fatih Yılmaz +2 more
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On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer‐Humbert polynomials are also discussed.
Tian-Xiao He +2 more
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