Results 81 to 90 of about 1,206 (140)
On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this paper, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results
Anatriello Giuseppina, Vincenzi Giovanni
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Generalized Jacobsthal-Narayana Numbers and Generalized Co-Jacobsthal-Narayana Numbers
Asian Journal of Advanced Research and ReportsThis paper introduces two innovative third-order recurrence sequences: the generalized Jacobsthal-Narayana sequence and the co-Jacobsthal-Narayana sequence. It examines their interrelated properties, including Binet’s formulas, generating functions, Simson’s formulas, and matrix representations, as well as their special subsequences.
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Journal of New Theory, 2021 In this study, new formulas for the nth power of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas special matrix sequences are established by using determinant and trace of the matrices.
Şükran Uygun
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Some results on one type of graph family with some special number sequences
AKCE International Journal of Graphs and Combinatorics, 2020 In this study, we introduce a new graph family. Then, we calculate eigenvalues of the adjacency and the Laplacian matrix of this graph family. Moreover, we show that the perfect matching number of this graph family equals to special second order ...
Emrullah Kirklar +2 more
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Fermatian row and column sums as a family of generalized integers [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce some feature of the Fermatian numbers. The finite sum formulas of these numbers is calculate. The exponential generating function of Fermatian numbers is found and some of its identities is calculated.
Anthony G. Shannon +2 more
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New families of Jacobsthal and Jacobsthal-Lucas numbers
, 2015 In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented.
Campos, Helena +4 more
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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers
Annales Mathematicae SilesianaeIn this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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Some Fibonacci congruences with square moduli [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci congruence with prime moduli have been extensively studied. Square moduli are obviously not prime numbers, so why study such congruences?
Anthony G. Shannon +2 more
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Complex Jacobsthal Numbers in Two Dimension
Sarajevo Journal of MathematicsIn this paper, we present a new approach to the generalization of Jacobsthal sequences to the complex plane. It is shown that the Jacobsthal numbers are generalized to two dimensions. For special entries of this new sequence, some relations to the classical Jacobsthal sequences are constructed.
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Non-Newtonian Jacobsthal and Jacobsthal-Lucas numbers: A new look
FilomatIn this study, we introduce a novel version of Jacobsthal and Jacobsthal-Lucas numbers, termed as non-Newtonian Jacobsthal and non-Newtonian Jacobsthal-Lucas numbers. We investigate various char-acteristics of these newly defined sequences. Additionally, we explore several formulas and identities such as Cassini?s identity, d?Ocagne?s identity, Binet?s
İlknur Yeşilyurt, Nilay Değirmen
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