The modified Pell and the modified \(k\)-Pell quaternions and octonions

DOI10.1007/s00006-015-0611-4zbMath1380.11010OpenAlexW1880286468MaRDI QIDQ297574

Paula Maria Machado Cruz Catarino

Publication date: 27 June 2016

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-015-0611-4

zbMATH Keywords

generating functionsquaternionsrecurrence relationsoctonionsmodified \(k\)-Pell numbersmodified Pell numbers

Mathematics Subject Classification ID

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

Related Items (19)

Split Pell and Pell-Lucas quaternions ⋮ On the bi-periodic Lucas octonions ⋮ On Jacobsthal and Jacobsthal-Lucas octonions ⋮ On dual \(k\)-Pell quaternions and octonions ⋮ On higher order Fibonacci hyper complex numbers ⋮ On Generalized Tribonacci Sedenions ⋮ On generalized Pentanacci quaternions ⋮ On a generalization for Fibonacci quaternions ⋮ On balancing and Lucas-balancing quaternions ⋮ Bicomplex \(k\)-Pell quaternions ⋮ Padovan and Perrin generalized quaternions ⋮ On hyper complex numbers with higher order Pell numbers components ⋮ Some remarks regarding \(l\)-elements defined in algebras obtained by the Cayley-Dickson process ⋮ New families of Fibonacci and Lucas octonions with \(Q\)-integer components ⋮ Some special number sequences obtained from a difference equation of degree three ⋮ ON k-JACOBSTHAL AND k-JACOBSTHAL-LUCAS OCTONIONS ⋮ The generalized bi-periodic Fibonacci quaternions and octonions ⋮ Some properties of Padovan quaternion ⋮ On quaternion Gaussian bronze Fibonacci numbers

Uses Software

• CLIFFORD

Cites Work

• The Pell quaternions and the Pell octonions
• Fibonacci generalized quaternions
• Split Fibonacci and Lucas octonions
• A note on \(h(x)\)-Fibonacci quaternion polynomials
• On Fibonacci quaternions
• The Fibonacci octonions
• On generalized Fibonacci quaternions and Fibonacci-Narayana quaternions
• On the Fibonacci \(k\)-numbers
• The \(k\)-Fibonacci sequence and the Pascal 2-triangle
• Computations with Clifford and Grassmann algebras
• SUMS, PRODUCTS AND IDENTITIES INVOLVING k-FIBONACCI AND k-LUCAS SEQUENCES
• On some identities and generating functions for k- Pell numbers
• Complex Fibonacci Numbers and Fibonacci Quaternions
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