Results 31 to 40 of about 105 (79)
On the intersection of two distinct $k$-generalized Fibonacci sequences [PDF]
, 2011 summary:Let $k\geq 2$ and define $F^{(k)}:=(F_n^{(k)})_{n\geq 0}$, the $k$-generalized Fibonacci sequence whose terms satisfy the recurrence relation $F_n^{(k)}=F_{n-1}^{(k)}+F_{n-2}^{(k)}+\cdots + F_{n-k}^{(k)}$, with initial conditions $0,0,\dots ,0,1$
Marques, Diego, Max A. Alekseyev
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Twisted rational zeros of linear recurrence sequences
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We introduce the notion of a twisted rational zero of a nondegenerate linear recurrence sequence (LRS). We show that any nondegenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that 1/3$1/3$ and −5/3$-5/3$ are the only twisted rational zeros that are not integral zeros.
Yuri Bilu +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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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
wiley +1 more source
Binomial tribonacci sums [PDF]
Discrete Mathematics Letters, 2021 Kunle Adegoke +2 more
doaj +1 more source
Root location for the characteristic polynomial of a Fibonacci type sequence
, 2023 summary:We analyse the roots of the polynomial $x^n-px^{n-1}-qx-1$ for $p\geqslant q\geqslant 1$. This is the characteristic polynomial of the recurrence relation $F_{k,p,q}(n) = pF_{k,p,q}(n- \nobreak 1) + qF_{k,p,q}(n-k + 1) + F_{k,p,q}(n-k)$ for $n ...
da Fonseca, Carlos M., Du, Zhibin
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, 2014 We rewrite the whole article and generalized our result with the help of second name ...
Raza, Zahid +2 more
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Formula for the $n$th $k$-Generalized Fibonacci-like Number
, 2022 In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by adding its ...
Balsomo, Alexander J. +4 more
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A search for Tribonacci-Wieferich primes [PDF]
, 2008 summary:Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present.
Klaška, Jiří
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, 2023 Bu tez beş bölümden oluşmaktadır. Birinci bölümde, Fibonacci ve Tribonacci sayıları ve polinomları konularında tez ile ilişkili yapılmış çalışmalara yer verildi. Tezde kullanılan yöntem ve teknikler ele alındı.
Arslan, Barış
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