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The Bernoullian of a Matrix. (A Generalization of the Bernoulli Numbers)

Esayas George Kundert (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si associano ad una matrice infinita di un certo tipo altre due matrici dello stesso tipo, dette rispettivamente bernoulliana e antibernoulliana di A. Si studiano alcune proprietà di queste matrici. Si ottiene in tal via una generalizzazione dei classici numeri di Bernoulli.

The k-Fibonacci matrix and the Pascal matrix

Sergio Falcon (2011)

Open Mathematics

We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.

The Pfaffian transform.

Austin, Tracale, Bantilan, Hans, Egge, Eric S., Jonas, Isao, Kory, Paul (2009)

Journal of Integer Sequences [electronic only]

The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q

Olcay Karaatlı (2016)

Acta Arithmetica

Let Vₙ(P,Q) denote the generalized Lucas sequence with parameters P and Q. For all odd relatively prime values of P and Q such that P² + 4Q > 0, we determine all indices n such that Vₙ(P,Q) = 7kx² when k|P. As an application, we determine all indices n such that the equation Vₙ = 21x² has solutions.

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