Results 41 to 50 of about 189 (146)
k‐Step Sum and m‐Step Gap Fibonacci Sequence
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 For two given integers k, m, we introduce the k‐step sumand m‐step gap Fibonacci sequence by presenting a recurrence formula that generates the nth term as the sum of k successive previous terms starting the sum at the mth previous term. Known sequences, like Fibonacci, tribonacci, tetranacci, and Padovan sequences, are derived for specific values of k,
Maria Adam +4 more
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On the Fibonacci Tiling and its Modern Ramifications
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well‐known Fibonacci chain to explain some of them, with pointers to various generalisations as well as ...
Michael Baake +2 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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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
Binomial tribonacci sums [PDF]
Discrete Mathematics Letters, 2021 Kunle Adegoke +2 more
doaj +1 more source
On Some New Sequence Spaces and Their Duals
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this study, we defined some new sequence spaces using regular Tribonacci matrix. We examined some properties of these spaces such as completeness, Schauder basis. We have identified α − , β−, and γ−duals of the newly created spaces.
Damla Barlak, Ömer Kişi
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Summing Formulas for Generalized Tribonacci Numbers
Universal Journal of Mathematics and Applications, 2020 In this paper, closed forms of the summation formulas for generalized Tribonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Tribonacci, Tribonacci-Lucas, Padovan, Perrin, Narayana and some other third order linear recurrance sequences.
openaire +6 more sources
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.Some boundedness and convergence properties of generalized Fibonacci’s‐type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so‐called (k, q) Fibonacci’s recurrence and the associated Fibonacci’s ratio recurrences are ...
Manuel De la Sen, V. Ravichandran
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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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