Displaying similar documents to “Binomial sequences”

Convolution of second order linear recursive sequences II.

Tamás Szakács (2017)

Communications in Mathematics

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We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

Rajkovic, Predrag M., Barry, Paul, Savic, Natasa (2012)

Mathematica Balkanica New Series

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MSC 2010: 11B83, 05A19, 33C45 This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.

The positivity problem for fourth order linear recurrence sequences is decidable

Pinthira Tangsupphathawat, Narong Punnim, Vichian Laohakosol (2012)

Colloquium Mathematicae

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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.

Binomials transformation formulae for scaled Fibonacci numbers

Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)

Open Mathematics

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The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.

Extension of classical sequences to negative integers

Benali Benzaghou, Daniel Barsky (2006)

Discussiones Mathematicae - General Algebra and Applications

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We give a method to extend Bell exponential polynomials to negative indices. This generalizes many results of this type such as the extension to negative indices of Stirling numbers or of Bernoulli numbers.