The Binet formula, sums and representations of generalized Fibonacci \(p\)-numbers

DOI10.1016/j.ejc.2007.03.004zbMath1138.11004OpenAlexW1964155221MaRDI QIDQ2426449

Emrah Kılıç

Publication date: 22 April 2008

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2007.03.004

zbMATH Keywords

generating functionmatrixBinet formulageneralized Fibonacci sequenceFibonacci \(p\)-numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

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Cites Work

• The golden section in measurement theory
• Theory of Binet formulas for Fibonacci and Lucas \(p\)-numbers
• The \(k\)-Fibonacci hyperbolic functions
• On the order-\(k\) generalized Lucas numbers
• The combinatorial power of the companion matrix
• The generalized Binet formula, representation and sums of the generalized order-\(k\) Pell numbers
• The generalized order-\(k\) Fibonacci-Pell sequence by matrix methods
• On the generalized order-\(k\) Fibonacci and Lucas numbers
• The Golden Shofar
• The continuous functions for the Fibonacci and Lucas \(p\)-numbers
• The \(k\)-Fibonacci sequence and the Pascal 2-triangle
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