On the computing of the generalized order-\(k\) Pell numbers in log time

DOI10.1016/J.AMC.2005.12.053zbMath1206.11150OpenAlexW2115492888MaRDI QIDQ945394

B. E. Eshmatov

Publication date: 12 September 2008

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.12.053

zbMATH Keywords

summatrix methodgeneralized order-\(k\) Pell number

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (3)

The infinite sum of the cubes of reciprocal pell numbers ⋮ On the order-\(m\) generalized Fibonacci \(k\)-numbers ⋮ The infinite sum of reciprocal Pell numbers

Cites Work

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• A fast algorithm for computing large Fibonacci numbers
• A presentation of the Fibonacci algorithm
• On the number of arithmetical operations for finding Fibonacci numbers
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• Computing Fibonacci numbers (and similarly defined functions) in log time
• An \(O(\log n)\) algorithm for computing the \(n\)th element of the solution of a difference equation
• An interative program to calculate Fibonacci numbers in O(log n) arithmetic operations
• Derivation of an \(O(k^ 2\log n)\) algorithm for computing order-k Fibonacci numbers from the \(O(k^ 3\log n)\) matrix multiplication method
• Computing sums of order-k Fibonacci numbers in log time
• The generalized Binet formula, representation and sums of the generalized order-\(k\) Pell numbers
• Generalized Fibonacci Numbers and Associated Matrices
• A Fast Algorithm for Computing Order-K Fibonacci Numbers

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