The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence [PDF]
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
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]
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
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The generalized Binet formula for $k$-bonacci numbers [PDF]
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]
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
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
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]
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]
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]
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