Generalized Fibonacci Numbers and Associated Matrices
From MaRDI portal
Publication:3287312
DOI10.2307/2308649zbMath0103.27203OpenAlexW4210823009MaRDI QIDQ3287312
Publication date: 1960
Published in: The American Mathematical Monthly (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2308649
Related Items (79)
Generalized hyper-Lucas numbers and applications ⋮ On \(F_3(k,n)\)-numbers of the Fibonacci type ⋮ The Galois group of \(x^{n}-x^{n-1}-\cdots-x-1\) ⋮ On Fermat and Mersenne numbers expressible as product of two \(k\)-Fibonacci numbers ⋮ Determinantal and permanental representations of Fibonacci type numbers and polynomials ⋮ A better upper bound on the bisection width of de Bruijn networks ⋮ Stability and sparsity in sets of natural numbers ⋮ Coincidence between \(k\)-Fibonacci numbers and products of two Fermat numbers ⋮ The Fibonacci family of iterative processes for solving nonlinear equations ⋮ On d-Fibonacci digraphs ⋮ On Fibonacci n-step numbers ⋮ Total graph interpretation of the numbers of the Fibonacci type ⋮ On new polynomial sequences constructed to each vertex in an \(n\)-gon ⋮ Gray codes for Fibonacci \(q\)-decreasing words ⋮ A Diophantine equation in $k$-Fibonacci numbers and repdigits ⋮ From Fibonacci sequence to the Golden ratio ⋮ A combinatorial interpretation of the generalized Fibonacci numbers ⋮ A Method for Uniformly Proving a Family of Identities ⋮ On the Fibonacci and Lucas \(p\)-numbers, their sums, families of bipartite graphs and permanents of certain matrices ⋮ On the order-\(m\) generalized Fibonacci \(k\)-numbers ⋮ On the characteristic polynomial of \((k,p)\)-Fibonacci sequence ⋮ An exponential equation involving k-Fibonacci numbers ⋮ On the distance between two algebraic numbers ⋮ Hydrodynamic limit for the \(d\)-facilitated exclusion process ⋮ Repdigits as sums of two generalized Lucas numbers ⋮ Invariant measures for the strong-facilitated exclusion process ⋮ \(k\)-Fibonacci numbers which are Padovan or Perrin numbers ⋮ The complete solution of the Diophantine equation \(\left(F_{n+1}^{(k)}\right)^x - \left(F_{n-1}^{(k)}\right)^x = F_m^{(k)}\) ⋮ On \(k\)-Fibonacci and \(k\)-Lucas numbers written as a product of two Pell numbers ⋮ Sums of the squares of terms of sequence \(\{u_n\}\) ⋮ A generalization of Lucas sequence and associated identities ⋮ Generalized Fibonacci numbers and Blackwell's renewal theorem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Aphid Sequences: Turning Fibonacci Numbers Inside Out ⋮ Multiplicative dependence between \(k\)-Fibonacci and \(k\)-Lucas numbers ⋮ SOME ALGEBRAICAL, COMBINATORIAL AND ANALYTICAL PROPERTIES OF PARAGRASSMANN VARIABLES ⋮ On the zero–multiplicity of a fifth-order linear recurrence ⋮ The polytopic-\(k\)-step Fibonacci sequences in finite groups ⋮ An identity relating Fibonacci and Lucas numbers of order \(k\) ⋮ On prime factors of the sum of two k-Fibonacci numbers ⋮ On the computing of the generalized order-\(k\) Pell numbers in log time ⋮ Return times of polynomials as meta-Fibonacci numbers ⋮ Multiplicative independence in \(k\)-generalized Fibonacci sequences ⋮ \(k\)-Fibonacci and \(k\)-Lucas numbers as product of two repdigits ⋮ Extending generalized Fibonacci sequences and their Binet-type formula ⋮ Broadcasting in DMA-bound bounded degree graphs ⋮ The generalized order-\(k\) Fibonacci-Pell sequence by matrix methods ⋮ On the generalized order-\(k\) Fibonacci and Lucas numbers ⋮ A new perspective on the integrability of Inozemtsev's elliptic spin chain ⋮ Yangian-invariant spin models and Fibonacci numbers ⋮ Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications ⋮ Repdigits in \(k\)-Lucas sequences ⋮ Information processing hierarchies ⋮ Limit of ratio of consecutive terms for general order-\(k\) linear homogeneous recurrences with constant coefficients ⋮ Unnamed Item ⋮ Generalized Fibonacci numbers and extreme value laws for the Rényi map ⋮ Unnamed Item ⋮ On the complexity of Fibonacci coding ⋮ On the \(k\)-generalized Fibonacci matrix \(Q_k\) ⋮ Repdigits as sums of two \(k\)-Fibonacci numbers ⋮ A new method to compute the terms of generalized order-\(k\) Fibonacci numbers ⋮ On the zero-multiplicity of the k-generalized Fibonacci sequence ⋮ Unnamed Item ⋮ Generalized order-\(k\) Fibonacci and Lucas functions ⋮ The plastic number and its generalized polynomial ⋮ Structure importance of consecutive-\(k\)-out-of-\(n\) systems ⋮ On some multinomial sums related to the Fibonacci type numbers ⋮ Companion sequences associated to ther-Fibonacci sequence: algebraic andcombinatorial properties ⋮ ON THE LARGEST PRIME FACTOR OF THE k-FIBONACCI NUMBERS ⋮ On the intersection of \(k\)-Lucas sequences and some binary sequences ⋮ On a generalization of the Pell sequence ⋮ On the representation of \(k\)-generalized Fibonacci and Lucas numbers ⋮ Efficiency of the polyphase merge and a related method ⋮ \(k\)-Lucas numbers and associated bipartite graphs ⋮ Coding theory on h(x) extension of m sequences for Fibonacci numbers ⋮ Q1 AND Q2 MATRIX REPRESENTATIONS OF GENERALIZED k-FIBONACCI SEQUENCE ⋮ k−Fibonacci numbers close to a power of 2
This page was built for publication: Generalized Fibonacci Numbers and Associated Matrices