Results 1 to 10 of about 1,028,977 (179)

The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence [PDF]

open access: diamondHittite Journal of Science and Engineering, 2016
In this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are ...
Ahmet Daşdemir
doaj   +6 more sources

The Binet formula, sums and representations of generalized Fibonacci p-numbers [PDF]

open access: bronzeEuropean Journal of Combinatorics, 2007
AbstractIn this paper, we consider the generalized Fibonacci p-numbers and then we give the generalized Binet formula, sums, combinatorial representations and generating function of the generalized Fibonacci p-numbers. Also, using matrix methods, we derive an explicit formula for the sums of the generalized Fibonacci p-numbers.
Emrah Kılıç
semanticscholar   +5 more sources

Extending generalized Fibonacci sequences and their binet-type formula [PDF]

open access: goldAdvances in Difference Equations, 2006
We study the extension problem of a given sequence defined by a finite order recurrence to a sequence defined by an infinite order recurrence with periodic coefficient sequence.
Saeki Osamu, Rachidi Mustapha
doaj   +6 more sources

The generalized Binet formula for $k$-bonacci numbers [PDF]

open access: diamondElemente der Mathematik, 2023
We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
Harold R. Parks, Dean C. Wills
semanticscholar   +3 more sources

A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity [PDF]

open access: green, 2013
We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\em not} involving determinants.
Takis Konstantopoulos
semanticscholar   +8 more sources

An Elementary Proof of the Generalization of the Binet Formula for $k$-bonacci Numbers

open access: greenarXiv.org, 2022
We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
Harold R. Parks, Dean C. Wills
semanticscholar   +5 more sources

A bijective proof of Muir's identity and the Cauchy-Binet formula

open access: bronzeLinear Algebra and its Applications, 1993
AbstractWe give a combinatorial proof of Muir's identity between permanents and determinants and of the Cauchy-Binet formula. Some related identities are also commented on.
Jiang Zeng
semanticscholar   +4 more sources

Algorithm for Constructing an Analogue of the Binet Formula [PDF]

open access: closedProgramming and Computer Software, 2020
In this paper, we describe an algorithm for constructing an analogue of the Binet formula, which is essential in deriving a functional relation to the classical Riemann zeta-function. The algorithm is implemented in the Maple computer algebra system. An example that illustrates the operation of the algorithm is presented.
V. I. Kuzovatov   +2 more
semanticscholar   +6 more sources

THE GENERALIZED BINET FORMULA, REPRESENTATION AND SUMS OF THE GENERALIZED ORDER-$k$ PELL NUMBERS [PDF]

open access: bronzeTaiwanese Journal of Mathematics, 2006
In this paper we give a new generalization of the Pell numbers in matrix representation. Also we extend the matrix representation and we show that the sums of the generalized order-k Pell numbers could be derived directly using this representation ...
Emrah Kılıç, Dursun Taşçı
semanticscholar   +6 more sources

Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]

open access: goldNotes on Number Theory and Discrete Mathematics
We will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma   +2 more
semanticscholar   +3 more sources

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