Results 41 to 50 of about 1,634,732 (135)
Non-Fisherian generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete MathematicsUsing biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
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On Power Sums Involving Lucas Functions Sequences
Mathematical Problems in Engineering, Volume 2017, Issue 1, 2017., 2017 We present some general formulas related to sum of powers, also with alternating sign, involving Lucas functions sequences. In particular, our formulas give a synthesis of various identities involving sum of powers of well‐known polynomial sequences such as Fibonacci, Lucas, Pell, Jacobsthal, and Chebyshev polynomials.
Stefano Barbero, Fazal M. Mahomed
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k-Jacobsthal and k-Jacobsthal Lucas matrix sequences
International Mathematical Forum, 2016 In this study, we consider sequences named k-Jacobsthal, k-Jacobsthal Lucas sequences. After that, by using these sequences, we dene kJacobsthal and k-Jacobsthal-Lucas matrix sequence at the same time. Finally we investigate some properties of these sequences, present some important relationship between k-Jacobsthal matrix sequence and kJacobsthal ...
S. Uygun, H. Eldogan
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A Generalization of Gaussian Balancing and Gaussian Balancing‐Lucas Numbers With Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this paper, we study a generalization of Gaussian balancing and Gaussian Lucas‐balancing numbers, we find their generating functions, Binet formulas, related matrix representation, and many other properties. Also, we provide some applications in cryptography.
T. Al-Asoully +2 more
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Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse ...
Li Liu, Zhaolin Jiang, Zidong Wang
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On the jacobsthal, horadam and geometric mean sequences [PDF]
, 2016 This paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.This paper, in considering aspects of the geometric mean sequence, offers ...
Rabago, Julius, F. T. +1 more
core
Sum of Squares of Mulatu Numbers That Are Powers of 2
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.In this work, we fully characterize all nonnegative integer solutions (n, m, a) to the Diophantine equation Mn2+Mm2=2a, where Mkk≥0 is the Mulatu sequence. The argument employs Matveev’s explicit lower bound for linear forms in logarithms of algebraic numbers together with the reduction technique of Dujella and Pethö to obtain an absolute upper bound ...
Ahmed Gaber +3 more
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VanderLaan Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, and g‐circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The
Hongyan Pan, Zhaolin Jiang, Shen Yin
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On the (r, p, k)-Generalized Jacobsthal Numbers and the Jacobsthal Fundamental Fibonacci System
Trends in Computational and Applied MathematicsThe main goal of this paper is to study the model of the sequences of (r, p, k)-generalized Jacobsthal numbers, by the approach based on the properties of its associated Jacobsthal fundamental Fibonacci system and its fundamental sequence.
M. Rachidi, F. Yilmaz
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On Jacobsthal and Jacobsthal‐Lucas Circulant Type Matrices
Abstract and Applied Analysis, Volume 2015, Issue 1, 2015., 2015 Circulant type matrices have become an important tool in solving fractional order differential equations. In this paper, we consider the circulant and left circulant and g‐circulant matrices with the Jacobsthal and Jacobsthal‐Lucas numbers. First, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix ...
Yanpeng Gong +3 more
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